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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

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Example Questions

Example Question #91 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 16 x + 79 and y = 31 x + 50

Possible Answers:

${x=- \frac{29}{15}}$

$\uptext{x}=6$

${x=\frac{29}{15}}$

$\uptext{x}=-5$

${x = \frac{58}{15}}$

Correct answer:

${x=\frac{29}{15}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

16 x + 79 = 31 x + 50

16 x + 79-79=31 x + 50-79

16 x=31 x - 29

16 x-31 x=31 x - 29-31 x

- 15 x=-29

$x=\frac{29}{15}$

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Example Question #92 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 26 x + 5 and y = 36 x - 87

Possible Answers:

${x = \frac{92}{5}}$

$\uptext{x}=-5$

${x=- \frac{46}{5}}$

${x=\frac{46}{5}}$

$\uptext{x}=6$

Correct answer:

${x=\frac{46}{5}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

26 x + 5 = 36 x - 87

26 x + 5-5=36 x - 87-5

26 x=36 x - 92

26 x-36 x=36 x - 92-36 x

- 10 x=-92

$x=\frac{46}{5}$

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Example Question #93 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 46 x + 47 and y = 27 x + 12

Possible Answers:

${x=\frac{35}{19}}$

$\uptext{x}=6$

${x=- \frac{35}{19}}$

${x = - \frac{70}{19}}$

$\uptext{x}=-5$

Correct answer:

${x=- \frac{35}{19}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

46 x + 47 = 27 x + 12

46 x + 47-47=27 x + 12-47

46 x=27 x - 35

46 x-27 x=27 x - 35-27 x

19 x=-35

$x=- \frac{35}{19}$

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Example Question #94 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 48 x + 35 and y = 23 x + 83

Possible Answers:

$\uptext{x}=-5$

${x=\frac{48}{25}}$

${x = \frac{96}{25}}$

${x=- \frac{48}{25}}$

$\uptext{x}=6$

Correct answer:

${x=\frac{48}{25}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

48 x + 35 = 23 x + 83

48 x + 35-35=23 x + 83-35

48 x=23 x + 48

48 x-23 x=23 x + 48-23 x

25 x=48

$x=\frac{48}{25}$

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Example Question #95 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 23 x - 53 and y = 41 x + 35

Possible Answers:

${x=\frac{44}{9}}$

${x = - \frac{88}{9}}$

$\uptext{x}=-5$

$\uptext{x}=6$

${x=- \frac{44}{9}}$

Correct answer:

${x=- \frac{44}{9}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

23 x - 53 = 41 x + 35

23 x - 53+53=41 x + 35+53

23 x=41 x + 88

23 x-41 x=41 x + 88-41 x

- 18 x=88

$x=- \frac{44}{9}$

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Example Question #96 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 20 x + 63 and y = 39 x + 74

Possible Answers:

$\uptext{x}=6$

${x=\frac{11}{19}}$

${x = - \frac{22}{19}}$

$\uptext{x}=-5$

${x=- \frac{11}{19}}$

Correct answer:

${x=- \frac{11}{19}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

20 x + 63 = 39 x + 74

20 x + 63-63=39 x + 74-63

20 x=39 x + 11

20 x-39 x=39 x + 11-39 x

- 19 x=11

$x=- \frac{11}{19}$

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Example Question #97 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 14 x - 90 and y = 18 x + 62

Possible Answers:

$\uptext{x}=-5$

{x=38}

{x=-38}

{x = -76}

$\uptext{x}=6$

Correct answer:

{x=-38}

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

14 x - 90 = 18 x + 62

14 x - 90+90=18 x + 62+90

14 x=18 x + 152

14 x-18 x=18 x + 152-18 x

- 4 x=152

x=-38

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Example Question #98 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 2 x + 3 and y = 28 x - 64

Possible Answers:

$\uptext{x}=6$

${x=\frac{67}{26}}$

${x = \frac{67}{13}}$

$\uptext{x}=-5$

${x=- \frac{67}{26}}$

Correct answer:

${x=\frac{67}{26}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

2 x + 3 = 28 x - 64

2 x + 3-3=28 x - 64-3

2 x=28 x - 67

2 x-28 x=28 x - 67-28 x

- 26 x=-67

$x=\frac{67}{26}$

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Example Question #99 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 2 x + 62 and y = 19 x - 29

Possible Answers:

${x=- \frac{91}{17}}$

${x = \frac{182}{17}}$

$\uptext{x}=-5$

$\uptext{x}=6$

${x=\frac{91}{17}}$

Correct answer:

${x=\frac{91}{17}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

2 x + 62 = 19 x - 29

2 x + 62-62=19 x - 29-62

2 x=19 x - 91

2 x-19 x=19 x - 91-19 x

- 17 x=-91

$x=\frac{91}{17}$

Report an Error

Example Question #100 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 22 x - 37 and y = 48 x - 11

Possible Answers:

{x=1}

$\uptext{x}=6$

{x=-1}

$\uptext{x}=-5$

{x = -2}

Correct answer:

{x=-1}

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

22 x - 37 = 48 x - 11

22 x - 37+37=48 x - 11+37

22 x=48 x + 26

22 x-48 x=48 x + 26-48 x

- 26 x=26

x=-1

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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #91 : Reasoning With Equations & Inequalities

Example Question #92 : Reasoning With Equations & Inequalities

Example Question #93 : Reasoning With Equations & Inequalities

Example Question #94 : Reasoning With Equations & Inequalities

Example Question #95 : Reasoning With Equations & Inequalities

Example Question #96 : Reasoning With Equations & Inequalities

Example Question #97 : Reasoning With Equations & Inequalities

Example Question #98 : Reasoning With Equations & Inequalities

Example Question #99 : Reasoning With Equations & Inequalities

Example Question #100 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

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