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Common Core: 6th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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Example Questions

Example Question #55 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 7 m - 20 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -48\\ \hline 8 & -76\\ \hline 16 & -132\\ \hline 18& -146\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -47\\ \hline 8 & -74\\ \hline 16 & -129\\ \hline 18& -142\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -48\\ \hline 8 & -152\\ \hline 16 & -264\\ \hline 18& -292\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -55\\ \hline 9 & -83\\ \hline 12 & -93\\ \hline 17& -129\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -48\\ \hline 8 & -76\\ \hline 16 & -132\\ \hline 18& -146\\ \hline \end{tabular}}$

Explanation:

In the equation - 7 m - 20 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Because we are given tables in our answer choices, we can plug in the given value for {m} from the table and use our equation from the question to see if that equals the value given for {n} in the table.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -47\\ \hline 8 & -74\\ \hline 16 & -129\\ \hline 18& -142\\ \hline \end{tabular}}$

{-7(4)+-20=-47}

{-28+-20=-47}

${-48\neq -47}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- 7 m - 20 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & -62\\ \hline 9 & -166\\ \hline 10 & -180\\ \hline 15& -250\\ \hline \end{tabular}}$

{-7(6)-20=-62}

{-42-20=-62}

{-62=-62}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-7(9)-20=-166}

{-63-20=-166}

${-83\neq -166}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -55\\ \hline 9 & -83\\ \hline 12 & -93\\ \hline 17& -129\\ \hline \end{tabular}}$

{-7(5)-20=-55}

{-35-20=-55}

{-55=-55}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-7(9)-20=-83}

{-63-20=-83}

{-83=-83}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-7(12)-20=-93}

{-84-20=-93}

${-104\neq -93}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -20\\ \hline 1 & -27\\ \hline 5 & -55\\ \hline 8& -76\\ \hline \end{tabular}}$

{-7(0)-20=-20}

{0-20=-20}

{-20=-20}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-7(1)-20=-27}

{-7-20=-27}

{-27=-27}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-7(5)-20=-55}

{-35-20=-55}

{-55=-55}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-7(8)-20=-76}

{-56+-20=-76}

{-76=-76}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #56 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 18 m + 6 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -30\\ \hline 10 & -174\\ \hline 12 & -199\\ \hline 17& -290\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -66\\ \hline 8 & -276\\ \hline 11 & -384\\ \hline 12& -420\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -65\\ \hline 8 & -136\\ \hline 11 & -189\\ \hline 12& -206\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -66\\ \hline 8 & -138\\ \hline 11 & -192\\ \hline 12& -210\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -66\\ \hline 8 & -138\\ \hline 11 & -192\\ \hline 12& -210\\ \hline \end{tabular}}$

Explanation:

In the equation - 18 m + 6 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -65\\ \hline 8 & -136\\ \hline 11 & -189\\ \hline 12& -206\\ \hline \end{tabular}}$

{-18(4)+6=-65}

{-72+6=-65}

${-66\neq -65}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- 18 m + 6 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 6 & -204\\ \hline 14 & -492\\ \hline 17& -600\\ \hline \end{tabular}}$

{-18(0)+6=6}

{0+6=6}

{6=6}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(6)+6=-204}

{-108+6=-204}

${-102\neq -204}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -30\\ \hline 10 & -174\\ \hline 12 & -199\\ \hline 17& -300\\ \hline \end{tabular}}$

{-18(2)+6=-30}

{-36+6=-30}

{-30=-30}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(10)+6=-174}

{-180+6=-174}

{-174=-174}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(12)+6=-199}

{-216+6=-199}

${-210\neq -199}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -12\\ \hline 11 & -192\\ \hline 13 & -228\\ \hline 16& -282\\ \hline \end{tabular}}$

{-18(1)+6=-12}

{-18+6=-12}

{-12=-12}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(11)+6=-192}

{-198+6=-192}

{-192=-192}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(13)+6=-228}

{-234+6=-228}

{-228=-228}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(16)+6=-282}

{-288+6=-282}

{-282=-282}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #651 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if 17 m + 15 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 15\\ \hline 10 & 185\\ \hline 13 & 247\\ \hline 15& 280\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 66\\ \hline 11 & 404\\ \hline 14 & 506\\ \hline 19& 676\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 66\\ \hline 11 & 202\\ \hline 14 & 253\\ \hline 19& 338\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 67\\ \hline 11 & 204\\ \hline 14 & 256\\ \hline 19& 342\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 66\\ \hline 11 & 202\\ \hline 14 & 253\\ \hline 19& 338\\ \hline \end{tabular}}$

Explanation:

In the equation 17 m + 15 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 67\\ \hline 11 & 204\\ \hline 14 & 256\\ \hline 19& 342\\ \hline \end{tabular}}$

{17(3)+15=67}

{51+15=67}

${66\neq 67}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {17 m + 15 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 49\\ \hline 5 & 200\\ \hline 16 & 574\\ \hline 17& 608\\ \hline \end{tabular}}$

{17(2)+15=49}

{34+15=49}

{49=49}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{17(5)+15=200}

{85+15=200}

${100\neq 200}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 15\\ \hline 10 & 185\\ \hline 13 & 247\\ \hline 15& 270\\ \hline \end{tabular}}$

{17(0)+15=15}

{0+15=15}

{15=15}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{17(10)+15=185}

{170+15=185}

{185=185}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{17(13)+15=247}

{221+15=247}

${236\neq 247}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 83\\ \hline 7 & 134\\ \hline 9 & 168\\ \hline 19& 338\\ \hline \end{tabular}}$

{17(4)+15=83}

{68+15=83}

{83=83}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{17(7)+15=134}

{119+15=134}

{134=134}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{17(9)+15=168}

{153+15=168}

{168=168}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{17(19)+15=338}

{323+15=338}

{338=338}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #58 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 7 m - 9 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -2\\ \hline 6 & 33\\ \hline 16 & 114\\ \hline 19& 134\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 5\\ \hline 12 & 150\\ \hline 14 & 178\\ \hline 19& 248\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 5\\ \hline 12 & 75\\ \hline 14 & 89\\ \hline 19& 124\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 6\\ \hline 12 & 77\\ \hline 14 & 92\\ \hline 19& 128\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 5\\ \hline 12 & 75\\ \hline 14 & 89\\ \hline 19& 124\\ \hline \end{tabular}}$

Explanation:

In the equation 7 m - 9 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 6\\ \hline 12 & 77\\ \hline 14 & 92\\ \hline 19& 128\\ \hline \end{tabular}}$

{7(2)+-9=6}

{14+-9=6}

${5\neq 6}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {7 m - 9 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 54\\ \hline 13 & 164\\ \hline 14 & 178\\ \hline 18& 234\\ \hline \end{tabular}}$

{7(9)-9=54}

{63-9=54}

{54=54}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(13)-9=164}

{91-9=164}

${82\neq 164}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -2\\ \hline 6 & 33\\ \hline 16 & 114\\ \hline 19& 134\\ \hline \end{tabular}}$

{7(1)-9=-2}

{7-9=-2}

{-2=-2}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(6)-9=33}

{42-9=33}

{33=33}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(16)-9=114}

{112-9=114}

${103\neq 114}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -9\\ \hline 9 & 54\\ \hline 11 & 68\\ \hline 12& 75\\ \hline \end{tabular}}$

{7(0)-9=-9}

{0-9=-9}

{-9=-9}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(9)-9=54}

{63-9=54}

{54=54}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(11)-9=68}

{77-9=68}

{68=68}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(12)-9=75}

{84+-9=75}

{75=75}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #59 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 7 m - 17 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 40\\ \hline 9 & 48\\ \hline 15 & 91\\ \hline 19& 120\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 39\\ \hline 9 & 92\\ \hline 15 & 176\\ \hline 19& 232\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -17\\ \hline 10 & 53\\ \hline 11 & 71\\ \hline 17& 112\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 39\\ \hline 9 & 46\\ \hline 15 & 88\\ \hline 19& 116\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 39\\ \hline 9 & 46\\ \hline 15 & 88\\ \hline 19& 116\\ \hline \end{tabular}}$

Explanation:

In the equation 7 m - 17 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 40\\ \hline 9 & 48\\ \hline 15 & 91\\ \hline 19& 120\\ \hline \end{tabular}}$

{7(8)+-17=40}

{56+-17=40}

${39\neq 40}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {7 m - 17 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -10\\ \hline 2 & -6\\ \hline 8 & 78\\ \hline 17& 204\\ \hline \end{tabular}}$

{7(1)-17=-10}

{7-17=-10}

{-10=-10}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(2)-17=-6}

{14-17=-6}

${-3\neq -6}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -17\\ \hline 10 & 53\\ \hline 11 & 71\\ \hline 17& 112\\ \hline \end{tabular}}$

{7(0)-17=-17}

{0-17=-17}

{-17=-17}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(10)-17=53}

{70-17=53}

{53=53}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(11)-17=71}

{77-17=71}

${60\neq 71}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 25\\ \hline 11 & 60\\ \hline 13 & 74\\ \hline 17& 102\\ \hline \end{tabular}}$

{7(6)-17=25}

{42-17=25}

{25=25}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(11)-17=60}

{77-17=60}

{60=60}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(13)-17=74}

{91-17=74}

{74=74}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{7(17)-17=102}

{119+-17=102}

{102=102}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #651 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if - 10 m - 5 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -5\\ \hline 1 & -15\\ \hline 8 & -74\\ \hline 12& -115\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -94\\ \hline 10 & -103\\ \hline 15 & -152\\ \hline 16& -161\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -95\\ \hline 10 & -105\\ \hline 15 & -155\\ \hline 16& -165\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -95\\ \hline 10 & -210\\ \hline 15 & -310\\ \hline 16& -330\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -95\\ \hline 10 & -105\\ \hline 15 & -155\\ \hline 16& -165\\ \hline \end{tabular}}$

Explanation:

In the equation - 10 m - 5 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -94\\ \hline 10 & -103\\ \hline 15 & -152\\ \hline 16& -161\\ \hline \end{tabular}}$

{-10(9)+-5=-94}

{-90+-5=-94}

${-95\neq -94}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- 10 m - 5 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -55\\ \hline 8 & -170\\ \hline 13 & -270\\ \hline 19& -390\\ \hline \end{tabular}}$

{-10(5)-5=-55}

{-50-5=-55}

{-55=-55}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-10(8)-5=-170}

{-80-5=-170}

${-85\neq -170}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -5\\ \hline 1 & -15\\ \hline 8 & -74\\ \hline 12& -115\\ \hline \end{tabular}}$

{-10(0)-5=-5}

{0-5=-5}

{-5=-5}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-10(1)-5=-15}

{-10-5=-15}

{-15=-15}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-10(8)-5=-74}

{-80-5=-74}

${-85\neq -74}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -5\\ \hline 7 & -75\\ \hline 12 & -125\\ \hline 15& -155\\ \hline \end{tabular}}$

{-10(0)-5=-5}

{0-5=-5}

{-5=-5}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-10(7)-5=-75}

{-70-5=-75}

{-75=-75}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-10(12)-5=-125}

{-120-5=-125}

{-125=-125}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-10(15)-5=-155}

{-150+-5=-155}

{-155=-155}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #61 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 11 m + 9 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -12\\ \hline 3 & -22\\ \hline 4 & -32\\ \hline 11& -108\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -13\\ \hline 3 & -24\\ \hline 4 & -35\\ \hline 11& -112\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -46\\ \hline 12 & -123\\ \hline 13 & -123\\ \hline 15& -146\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -13\\ \hline 3 & -48\\ \hline 4 & -70\\ \hline 11& -224\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -13\\ \hline 3 & -24\\ \hline 4 & -35\\ \hline 11& -112\\ \hline \end{tabular}}$

Explanation:

In the equation - 11 m + 9 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -12\\ \hline 3 & -22\\ \hline 4 & -32\\ \hline 11& -108\\ \hline \end{tabular}}$

{-11(2)+9=-12}

{-22+9=-12}

${-13\neq -12}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- 11 m + 9 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 9\\ \hline 5 & -92\\ \hline 6 & -114\\ \hline 10& -202\\ \hline \end{tabular}}$

{-11(0)+9=9}

{0+9=9}

{9=9}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-11(5)+9=-92}

{-55+9=-92}

${-46\neq -92}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -46\\ \hline 12 & -123\\ \hline 13 & -123\\ \hline 15& -156\\ \hline \end{tabular}}$

{-11(5)+9=-46}

{-55+9=-46}

{-46=-46}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-11(12)+9=-123}

{-132+9=-123}

{-123=-123}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-11(13)+9=-123}

{-143+9=-123}

${-134\neq -123}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -24\\ \hline 5 & -46\\ \hline 10 & -101\\ \hline 12& -123\\ \hline \end{tabular}}$

{-11(3)+9=-24}

{-33+9=-24}

{-24=-24}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-11(5)+9=-46}

{-55+9=-46}

{-46=-46}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-11(10)+9=-101}

{-110+9=-101}

{-101=-101}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-11(12)+9=-123}

{-132+9=-123}

{-123=-123}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #62 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - m + 11 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 7\\ \hline 10 & 1\\ \hline 14 & -3\\ \hline 19& -8\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 7\\ \hline 10 & 2\\ \hline 14 & -6\\ \hline 19& -16\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 8\\ \hline 7 & 4\\ \hline 10 & 12\\ \hline 15& 6\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 8\\ \hline 10 & 3\\ \hline 14 & 0\\ \hline 19& -4\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 7\\ \hline 10 & 1\\ \hline 14 & -3\\ \hline 19& -8\\ \hline \end{tabular}}$

Explanation:

In the equation - m + 11 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 8\\ \hline 10 & 3\\ \hline 14 & 0\\ \hline 19& -4\\ \hline \end{tabular}}$

{-1(4)+11=8}

{-4+11=8}

${7\neq 8}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- m + 11 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 7\\ \hline 7 & 8\\ \hline 11 & 0\\ \hline 14& -6\\ \hline \end{tabular}}$

{-1(4)+11=7}

{-4+11=7}

{7=7}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-1(7)+11=8}

{-7+11=8}

${4\neq 8}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 8\\ \hline 7 & 4\\ \hline 10 & 12\\ \hline 15& -4\\ \hline \end{tabular}}$

{-1(3)+11=8}

{-3+11=8}

{8=8}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-1(7)+11=4}

{-7+11=4}

{4=4}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-1(10)+11=12}

{-10+11=12}

${1\neq 12}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 11\\ \hline 11 & 0\\ \hline 12 & -1\\ \hline 13& -2\\ \hline \end{tabular}}$

{-1(0)+11=11}

{0+11=11}

{11=11}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-1(11)+11=0}

{-11+11=0}

{0=0}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-1(12)+11=-1}

{-12+11=-1}

{-1=-1}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-1(13)+11=-2}

{-13+11=-2}

{-2=-2}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #63 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 18 m - 8 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -79\\ \hline 12 & -222\\ \hline 14 & -257\\ \hline 16& -292\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -26\\ \hline 7 & -134\\ \hline 11 & -195\\ \hline 16& -286\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -80\\ \hline 12 & -448\\ \hline 14 & -520\\ \hline 16& -592\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -80\\ \hline 12 & -224\\ \hline 14 & -260\\ \hline 16& -296\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -80\\ \hline 12 & -224\\ \hline 14 & -260\\ \hline 16& -296\\ \hline \end{tabular}}$

Explanation:

In the equation - 18 m - 8 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -79\\ \hline 12 & -222\\ \hline 14 & -257\\ \hline 16& -292\\ \hline \end{tabular}}$

{-18(4)+-8=-79}

{-72+-8=-79}

${-80\neq -79}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- 18 m - 8 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -44\\ \hline 5 & -196\\ \hline 8 & -304\\ \hline 13& -484\\ \hline \end{tabular}}$

{-18(2)-8=-44}

{-36-8=-44}

{-44=-44}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(5)-8=-196}

{-90-8=-196}

${-98\neq -196}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -26\\ \hline 7 & -134\\ \hline 11 & -195\\ \hline 16& -286\\ \hline \end{tabular}}$

{-18(1)-8=-26}

{-18-8=-26}

{-26=-26}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(7)-8=-134}

{-126-8=-134}

{-134=-134}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(11)-8=-195}

{-198-8=-195}

${-206\neq -195}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -44\\ \hline 3 & -62\\ \hline 6 & -116\\ \hline 12& -224\\ \hline \end{tabular}}$

{-18(2)-8=-44}

{-36-8=-44}

{-44=-44}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(3)-8=-62}

{-54-8=-62}

{-62=-62}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(6)-8=-116}

{-108-8=-116}

{-116=-116}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(12)-8=-224}

{-216+-8=-224}

{-224=-224}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #64 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 19 m + 17 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 74\\ \hline 6 & 131\\ \hline 11 & 237\\ \hline 16& 331\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 56\\ \hline 8 & 171\\ \hline 10 & 210\\ \hline 14& 287\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 55\\ \hline 8 & 338\\ \hline 10 & 414\\ \hline 14& 566\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 55\\ \hline 8 & 169\\ \hline 10 & 207\\ \hline 14& 283\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 55\\ \hline 8 & 169\\ \hline 10 & 207\\ \hline 14& 283\\ \hline \end{tabular}}$

Explanation:

In the equation 19 m + 17 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 56\\ \hline 8 & 171\\ \hline 10 & 210\\ \hline 14& 287\\ \hline \end{tabular}}$

{19(2)+17=56}

{38+17=56}

${55\neq 56}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {19 m + 17 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 112\\ \hline 8 & 338\\ \hline 10 & 414\\ \hline 13& 528\\ \hline \end{tabular}}$

{19(5)+17=112}

{95+17=112}

{112=112}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{19(8)+17=338}

{152+17=338}

${169\neq 338}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 74\\ \hline 6 & 131\\ \hline 11 & 237\\ \hline 16& 321\\ \hline \end{tabular}}$

{19(3)+17=74}

{57+17=74}

{74=74}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{19(6)+17=131}

{114+17=131}

{131=131}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{19(11)+17=237}

{209+17=237}

${226\neq 237}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 36\\ \hline 4 & 93\\ \hline 8 & 169\\ \hline 9& 188\\ \hline \end{tabular}}$

{19(1)+17=36}

{19+17=36}

{36=36}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{19(4)+17=93}

{76+17=93}

{93=93}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{19(8)+17=169}

{152+17=169}

{169=169}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{19(9)+17=188}

{171+17=188}

{188=188}

All of these values were correct for our equation; thus, this table is our correct answer.

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Common Core: 6th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #55 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #56 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #651 : Expressions & Equations

Example Question #58 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #59 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #651 : Expressions & Equations

Example Question #61 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #62 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #63 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #64 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

All Common Core: 6th Grade Math Resources

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