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Algebra 1 : How to solve absolute value equations

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Example Questions

Example Question #21 : How To Solve Absolute Value Equations

$3(x+1)^2=\left | x+1\right |. \textup{Which is not a solution?}$

Possible Answers:

$-\frac{5}{3}$

$\textup{None of the above.}$

$-\frac{2}{3}$

$-\frac{4}{3}$

Correct answer:

$-\frac{5}{3}$

Explanation:

$\\ \textup{We get rid of the absolute value by solving the two equations }\\3(x+1)^2=x+1\\\textup{and}\\3(x+1)^2=-(x+1)\\\textup{If } x\neq1\textup{ we can divide in both equations the two sides by }\\ x+1 \textup{ and obtain }\\ 3(x+1)=1 \\\textup{ and }}\\ 3(x+1)=-1 \\\textup{ which give}}\\ \textup{the solutions } x=-\frac{2}{3} \textup{ and } x=-\frac{4}{3}.$

$\textup{If } x=-1, \textup{both sides are equal to 0, so } -1 \textup{ is another solution.}$

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Example Question #22 : How To Solve Absolute Value Equations

Solve for all possible values of .

$\left |3x-2 \right | = -4$

Possible Answers:

x=-2,x=2/3

x=3,x=-2

x=2/3,x=-3

x=2,x=-3

x=-2/3, x=2

Correct answer:

x=-2/3, x=2

Explanation:

$\left |3x-2 \right |=-4$

First, ignore absolute value signs and solve for x.

3x-2=-4

3x=-2

x=-2/3

Now, for the other solution, ignore absolute value signs and change the sign of the right side of the equation. Solve for x.

3x-2=4

3x=6

x=2

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Example Question #23 : How To Solve Absolute Value Equations

Solve for all values of .

$\left | 4x\right |-2=10$

Possible Answers:

x=3,x=2

x=-2,x=3

x=2,x=-2

x=3,x=-3

x=0,x=3

Correct answer:

x=3,x=-3

Explanation:

First, make sure to have the absolute value part of the equation by itself on the left side.

$\left | 4x\right |-2=10$

$\left | 4x\right |=12$

Now solve for both x values.

4x=12

x=3

Change the side of the right hand side to find the other value of x.

4x=-12

x=-3

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Example Question #24 : How To Solve Absolute Value Equations

Solve for .

$\left | 2x-3\right | +2=5$

Possible Answers:

x = 0,3

x = 0, -3

x = 3, -3

x = 1, -3

x = 0, 1

Correct answer:

x = 0,3

Explanation:

The question is asking for the value of . To isolate , we must first isolate the absolute value expression.

$\left | 2x-3 \right | = 3$

The absolute value bars give a positive value to the result of the expression within. This means the real value of the inner expression could be positive or negative. To find the two values of , create the two possible equations.

2x-3=3 $\boldsymbol{\mathbf{OR}}$ 2x-3=-3

Balance the equations to find .

2x-3=3

2x=6

x=3

2x-3=-3

2x=0

x=0

Therefore, x= 0 and x=3

Also written as x= 0,3 .

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Example Question #24 : How To Solve Absolute Value Equations

Solve for .

$\left | x\right |=10$

Possible Answers:

$\pm1$

$\pm10$

Correct answer:

$\pm10$

Explanation:

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

x=10

-x=10

Divide both sides by , we get x=-10 .

Final answer is $\pm10$ .

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Example Question #25 : How To Solve Absolute Value Equations

Solve for .

$\left | x+5\right |=2$

Possible Answers:

-3, -7

3, 7

Correct answer:

-3, -7

Explanation:

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

x+5=2

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

-(x+5)=2

Distribute the negative sign to get -x-5=2 .

Add both sides by and divide both sides by to get x=-7 .

Final answer is -3, -7 .

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Example Question #27 : How To Solve Absolute Value Equations

Solve for .

$\left | x-4\right |=12$

Possible Answers:

-8, 16

-8, -12

-12, 16

Correct answer:

-8, 16

Explanation:

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

x-4=12

Add both sides by , we get x=16 .

-(x-4)=12

Distribute the negative sign to get -x+4=12 .

Subtract both sides by and divide both sides by to get x=-8 .

Final answer is -8, 16 .

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Example Question #26 : How To Solve Absolute Value Equations

Solve for .

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

Possible Answers:

0, -12

Correct answer:

0, -12

Explanation:

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

6+x=6

Subtract both sides by , we get x=0 .

-(6+x)=6

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

Add both sides by and divide both sides by to get x=-12 .

Final answer is 0, -12 .

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Example Question #27 : How To Solve Absolute Value Equations

Solve for .

$\left | \frac{x}{3} \right |=4$

Possible Answers:

$\pm12$

$\frac{3}{4}$

$\frac{4}{3}$

Correct answer:

$\pm12$

Explanation:

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

$\frac{x}{3}=4$

Cross multiply and we get x=12 .

$\frac{-x}{3}=4$

Cross multiply and divide both sides by , we get x=-12 .

Final answer is $\pm12$ .

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Example Question #28 : How To Solve Absolute Value Equations

Solve for .

$3\left | x\right |=6$

Possible Answers:

$\pm2$

$\pm3$

Correct answer:

$\pm2$

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=2

-x=2

Divide both sides by , we get x=-2 .

Final answer is $\pm2$ .

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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 #21 : How To Solve Absolute Value Equations

Example Question #22 : How To Solve Absolute Value Equations

Example Question #23 : How To Solve Absolute Value Equations

Example Question #24 : How To Solve Absolute Value Equations

Example Question #24 : How To Solve Absolute Value Equations

Example Question #25 : How To Solve Absolute Value Equations

Example Question #27 : How To Solve Absolute Value Equations

Example Question #26 : How To Solve Absolute Value Equations

Example Question #27 : How To Solve Absolute Value Equations

Example Question #28 : How To Solve Absolute Value Equations

All Algebra 1 Resources

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