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High School Math : How to solve two-step equations with integers in pre-algebra

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Example Questions

Example Question #21 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

$\frac{x}{7}-64=-32$

Possible Answers:

x=224

x=-198

x=198

x=256

Correct answer:

x=224

Explanation:

To perform a two step algebra problem with addition and division we must remove the numbers from so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being subtracted so we must add the number, , to each side of the equation

$\frac{x}{7}-64+64=-32+64$

Perform the math so our equation becomes

$\frac{x}{7}=32$

Then we multiply each side of the equation by the number that is under to get by itself

$7\cdot \left(\frac{x}{7}\right)=7\cdot (32)$

Perform the math to find the answer x=224

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Example Question #431 : High School Math

Solve for if

4(x-7)=20

Possible Answers:

x=13

x=8

x=14

x=12

Correct answer:

x=12

Explanation:

The problem above is a two-step algebra problem with distribution.

To solve you must first distribute the outside of the parentheses into both of the numbers inside my multiplying 4x-28=20

Then we must get our variable, , by itself.

To do this we must add the number, , to each side of the equation

4x-28+28=20+28

Perform the math so our equation becomes 4x=48 .

Then we divide each side of the equation by the number that is in front of to get by itself

$\frac{4x}{4}=\frac{48}{4}$

Perform the math to find the answer x=12

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Example Question #23 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

x+8=4x+32

Possible Answers:

x=-21

x=3

x=-8

x=15

Correct answer:

x=-8

Explanation:

When there are variables and numbers on each side of the equation, to solve we must mathematically move the variables onto one side and the numbers onto the other.

To do this we put all of the variables on the right side of the equal sign by subtracting from the right and left side of the equation to have

x-x+8=4x-x+32

When adding or subtracting variables you only add or subtract the numbers in front of the variables. If there is no number the number value is .

Perform the math:

8=3x+32

Then to get all of the integers to the left side we will subtract from the right and left side of the equation to have

8-32=3x+32-32

Perform the math:

-24=3x

At this point we must divide each side of the equation by the number that is in front of to get by itself $\frac{-24}{3}=\frac{3x}{3}$

Perform the math to find the answer $\frac{-24}{3}=x$

The answer is x=-8 .

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Example Question #23 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

3x+17=41

Possible Answers:

x=9

x=6

x=8

x=7

Correct answer:

x=8

Explanation:

To perform a two-step algebra problem with addition and multiplication we must remove the numbers from so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being added so we must subtract the number, , from each side of the equation: 3x+17-17=41-17

Perform the math so that our equation becomes 3x=24 .

Then we divide each side of the equation by the number that is in front of , , to get by itself

$\frac{3x}{3}=\frac{24}{3}$

Perform the math to find the answer x=8

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Example Question #21 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

$\frac{x}{4}-34=6$

Possible Answers:

x=32

x=88

x=144

x=160

Correct answer:

x=160

Explanation:

To perform a two-step algebra problem with addition and division we must remove the numbers from so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being subtracted so we must add the number, , to each side of the equation

$\frac{x}{4}-34+34=6+34$

Perform the math so our equation becomes

$\frac{x}{4}=40$

Then we multiply each side of the equation by the number that is under , , to get by itself $x=4\cdot 40$

Perform the math to find the answer x=160

Report an Error

Example Question #22 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

3(x+5)=45

Possible Answers:

x=30

x=15

x=10

x=25

Correct answer:

x=10

Explanation:

The problem above is a two-step algebra problem with distribution.

To solve you must first distribute the outside of the parentheses to both of the numbers inside my multiplying.

Perform the multiplication with and each of the individual numbers to get our new equation, 3x+15=45

Then we must get our variable, , by itself.

We must subtract the number, , from each side of the equation 3x+15-15=45-15

Perform the math so our equation becomes 3x=30 .

Then we divide each side of the equation by the number that is in front of to get by itself

$\frac{3x}{3}=\frac{30}{3}$

Solve to find the answer x=10 .

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Example Question #432 : High School Math

Solve for if

x+78=3x+54

Possible Answers:

x=12

x=11

x=13

x=15

Correct answer:

x=12

Explanation:

When there are variables and numbers on each side of the equation, to solve we must move the variables onto one side and the numbers onto the other.

To do this we put all of the variables on the right side of the equal sign by subtracting from the left and right side of the equation to have x-x+78=3x-x+54

When adding or subtracting variables you only add or subtract the numbers in front of the variables. If there is no number the number value is .

Perform the math: 78=2x+54 .

Then to get all of the integers to the left side we will subtract from the right and left side of the equation to have

78-54=2x+54-54

Perform the math: 24=2x

At this point we must divide each side of the equation by the number that is in front of to get by itself $\frac{24}{2}=\frac{2x}{2}$

Perform the math to find the answer

$\frac{24}{2}=x$

The answer is x=12 .

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Example Question #24 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if 12x+237=381 .

Possible Answers:

x=144

x=44

x=12

x=241

Correct answer:

x=12

Explanation:

To perform a two step algebra problem with addition and multiplication, we must remove the constants from so that it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being added so we must subtract the number, 237 , from each side of the equation: 12x+237-237=381-237

Perform the math to make our equation look like 12x=144 .

Then, we divide each side of the equation by the constant attached to to get by itself: $\frac{12x}{12}=\frac{144}{12}$

The division yields x=12 .

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Example Question #21 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if $\frac{x}{11}-10=2$ .

Possible Answers:

x=391

x=88

x=132

x=16

Correct answer:

x=132

Explanation:

To perform a two step algebra problem with addition and division, we must remove the constants from so that it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being subtracted, so we must add the number, , to each side of the equation: $\frac{x}{11}-10+10=2+10$

Perform the math to see that that our equation looks like $\frac{x}{11}=12$ .

Then we multiply each side of the equation by the constant attached to to get by itself: $\frac{x}{11}(11)=12(11)$

Perform the multiplication to find x=132 .

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Example Question #30 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if -8(-x-3)=64 .

Possible Answers:

x=3

x=5

x=7

x=4

Correct answer:

x=5

Explanation:

The problem above is a two-step algebra problem with distribution.

To solve you must first distribute the outside of the parentheses through the numbers inside by multiplying.

Remember, when you distribute a negative, both of the numbers inside the parentheses are being multiplied by a negative number, so they must both flip signs.

Our problem now looks like 8x+24=64 .

Then we must isolate our variable, .

We must subtract the number, , from each side of the equation: 8x+24-24=64-24

Perform the math so that our equation looks like 8x=40 .

Then divide each side of the equation by the constant attached to to get by itself: $\frac{8x}{8}=\frac{40}{8}$

Solve the math to find the answer, x=5 .

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High School Math : How to solve two-step equations with integers in pre-algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #21 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #431 : High School Math

Example Question #23 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #23 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #21 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #22 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #432 : High School Math

Example Question #24 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #21 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #30 : How To Solve Two Step Equations With Integers In Pre Algebra

All High School Math Resources

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