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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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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Example Question #31 : How To Solve Absolute Value 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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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

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

Example Question #31 : How To Solve Absolute Value 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

All Algebra 1 Resources

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