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Algebra 1 : How to solve absolute value equations

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Example Questions

Example Question #861 : Linear Equations

Solve for .

$2\left | x+4\right |=18$

Possible Answers:

$\pm9$

5, -13

Correct answer:

5, -13

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

Let's first divide both sides by .

We have:

x+4=9

Subtract both sides by , we get x=5 .

-(x+4)=9

Distribute the negative sign to get -x-4=9 .

Add both sides by and divide both sides by to get x=-13 .

Final answer is 5, -13 .

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Example Question #32 : How To Solve Absolute Value Equations

Solve for .

$\left | \frac{x+2}{4} \right |=5$

Possible Answers:

$\pm20$

18, -22

Correct answer:

18, -22

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

$\frac{x+2}{4}=5$

Cross multiply and we get x+2=20 .

Then subtract both sides by to get x=18 .

$-\left(\frac{x+2}{4}\right)=5$

Let's divide both sides by to make the math easier and then cross multiply.

We get x+2=-20 .

Subtract both sides by to get x=-22 .

Final answer is 18, -22 .

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Example Question #33 : How To Solve Absolute Value Equations

Solve for .

$\left | x+7\right |-3=12$

Possible Answers:

8, -22

$\pm15$

Correct answer:

8, -22

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

First add to both sides.

x+7=15

Subtract both sides by , we get x=8 .

-(x+7)=15

Distribute the negative sign to get -x-7=15 .

Add both sides by and divide both sides by to get x=-22 .

Final answer is 8, -22 .

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Example Question #34 : How To Solve Absolute Value Equations

Solve for .

$2\left | x+6\right |-4=18$

Possible Answers:

5, -17

Correct answer:

5, -17

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

First add to both sides.

$2\left |x+6 \right |=22$

Divide both sides by , we get $\left |x+6 \right |=11$ .

x+6=11

Subtract both sides by , we get x=5 .

-(x+6)=11

Distribute the negative sign to get -x-6=11 .

Add both sides by and divide both sides by to get x=-17 .

Final answer is 5, -17 .

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Example Question #35 : How To Solve Absolute Value Equations

Solve for .

$2-3\left | x+7\right |=-10$

Possible Answers:

-3, -11

Correct answer:

-3, -11

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

First subtract to both sides.

$-3\left |x+7 \right |=-12$

Divide both sides by , we get $\left |x+7 \right |=4$ .

x+7=4

Subtract both sides by , we get x=-3 .

-(x+7)=4

Distribute the negative sign to get -x-7=4 .

Add both sides by and divide both sides by to get x=-11 .

Final answer is -3, -11 .

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Example Question #36 : How To Solve Absolute Value Equations

Solve for

$\left | \frac{x+2}{3} \right |-6=1$

Possible Answers:

19, -23

$\pm21$

Correct answer:

19, -23

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

First add to both sides.

$\left | \frac{x+2}{3} \right |=7$

Multiply both sides by , we get $\left |x+2 \right |=21$ .

x+2=21

Subtract both sides by , we get x=21 .

-(x+2)=21

Distribute the negative sign to get -x-2=21 .

Add both sides by and divide both sides by to get x=-23 .

Final answer is 19, -23 .

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Example Question #31 : How To Solve Absolute Value Equations

Solve for .

$\left | x\right |=19$

Possible Answers:

$\pm19$

Correct answer:

$\pm19$

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

x=19 and -x=19 .

For the second equation divide both sides by to get x=-19 .

Thus, our solutions for are,

$x=\pm19$ .

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Example Question #32 : How To Solve Absolute Value Equations

Solve for .

$\left | -x\right |=10$

Possible Answers:

$\pm10$

Correct answer:

$\pm10$

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

-(-x)=10 and -x=10

The two negatives become positive for the first equation.

x=10

For the second equation divide both sides by to get x=-10 .

Therefore, the solutions are

$x=\pm10$ .

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Example Question #39 : How To Solve Absolute Value Equations

Solve for .

$\left | x+6\right |=19$

Possible Answers:

13, -25

-13, -25

Correct answer:

13, -25

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

x+6=19 and -(x+6)=19 .

For the first equation subtract on both sides.

x=13

For the second equation, by distributing the negative sign, we have:

-x-6=19

From here add to both sides and divide both sides by , we get x=-25 .

Therefore, the solutions are,

x=13, -25 .

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Example Question #40 : How To Solve Absolute Value Equations

Solve for .

$\left | x+4\right |=2$

Possible Answers:

$\pm2$

2, 6

-2, -6

Correct answer:

-2, -6

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

x+4=2 and -(x+4)=2 .

For the first equation subtract on both sides to get x=-2 .

Remember since is greater than and is negative, our answer is negative. We treat as a subtraction problem.

For the second equation, by distributing the negative sign, we have: -x-4=2 .

From here add to both sides and divide both sides by to get x=-6 .

Therefore, the solutions are,

x=-2, -6 .

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Algebra 1 : How to solve absolute value equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #861 : Linear Equations

Example Question #32 : How To Solve Absolute Value Equations

Example Question #33 : How To Solve Absolute Value Equations

Example Question #34 : How To Solve Absolute Value Equations

Example Question #35 : How To Solve Absolute Value Equations

Example Question #36 : How To Solve Absolute Value Equations

Example Question #31 : How To Solve Absolute Value Equations

Example Question #32 : How To Solve Absolute Value Equations

Example Question #39 : How To Solve Absolute Value Equations

Example Question #40 : How To Solve Absolute Value Equations

All Algebra 1 Resources

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