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Algebra 1 : How to solve absolute value equations

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Example Question #41 : How To Solve Absolute Value Equations

Solve for .

$\left | x\right |+3=9$

Possible Answers:

$\pm12$

$\pm6$

Correct answer:

$\pm6$

Explanation:

To solve this problem we first need to isolate the variable on one side with all other constants on the other side.

$\left | x\right |+3=9$

To accomplish this perform the opposite opperation therefore subtract on both sides.

$\left | x\right |=6$

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

Therefore, we will set up two equations to solve,

x=6 and -x=6 .

For the second equation divide both sides by to get x=-6 .

Therefore the solutions are,

$x=\pm6$ .

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Example Question #42 : How To Solve Absolute Value Equations

Solve for .

$\left | x-8\right |=17$

Possible Answers:

$\pm25$

$\pm9$

-9, 25

Correct answer:

-9, 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-8=17 and -(x-8)=17 .

For the first equation add to both sides to get x=25 .

For the second equation, by distributing the negative sign, we have: -x+8=17 .

Now subtract to both sides and divide both sides by to get x=-9 .

Therefore, the solutions are,

x=-9, 25 .

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Example Question #43 : How To Solve Absolute Value Equations

Solve for .

$\left | x-10\right |=8$

Possible Answers:

2, 18

Correct answer:

2, 18

Explanation:

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

Therefore, we will create two separate equations to solve

Equation 1:

x-10=8

Add to both sides. x=18

Equation 2:

-(x-10)=8

By distributing the negative sign, we have: -x+10=8 Subtract to both sides and divide both sides by , we get x=2 . Remember, since is greater than and is negative, our answer is negative and we treat as a normal subtraction problem.

Therefore, the solutions are,

x=2, 18 .

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Example Question #44 : How To Solve Absolute Value Equations

Solve for .

$5\left | x\right |=95$

Possible Answers:

$\pm19$

Correct answer:

$\pm19$

Explanation:

First we will need to isolate the variable on one side of the equation and all other constants on the other side.

$5\left | x\right |=95$

Divide both sides by .

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

Therefore, we will create two separate equations to solve.

Equation 1:

x=19

Equation 2:

-x=19

Divide on both sides to get x=-19 .

Therefore, the solutions are,

$x=\pm19$ .

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Example Question #45 : How To Solve Absolute Value Equations

Solve for .

$\left | 3x\right |=78$

Possible Answers:

$\pm78$

$\pm26$

Correct answer:

$\pm26$

Explanation:

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

Therefore, we will create two separate equations to solve.

Equation 1:

3x=78

Divide on both sides. x=26 .

Equation 2:

-3x=78

Divide on both sides. x=-26 .

Therefore, the solutions are,

$x=\pm26$ .

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Example Question #46 : How To Solve Absolute Value Equations

Solve for .

$\left | 4x+5\right |=37$

Possible Answers:

$\pm8$

$\pm10.5$

8, -10.5

-10.5

Correct answer:

8, -10.5

Explanation:

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

Therefore, we will create two separate equations to solve.

Equation 1: 4x+5=37

Subtract to both sides. Then divide to both sides. x=8

Equation 2: -(4x+5)=37

By distributing the negative sign, we have: -4x-5=37

Add to both sides and divide both sides by , we get x=-10.5 .

Therefore, the solutions are,

x=-10.5, 8 .

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Example Question #47 : How To Solve Absolute Value Equations

Solve for .

$\left | \frac{x}{6} \right |=8$

Possible Answers:

$\pm48$

$\pm1.5$

1.5

Correct answer:

$\pm48$

Explanation:

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

Therefore, we will create two separate equations to solve.

Equation 1:

$\frac{x}{6} =8$

Multiply on both sides. x=48 .

Equation 2:

$\frac{-x}{6}=8$

Multiply on both sides and divide on both sides. x=-48 .

Therefore, the solutions are, $x=\pm48$ .

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Example Question #41 : How To Solve Absolute Value Equations

Solve for .

$\left | \frac{x}{7}+3 \right |=9$

Possible Answers:

42, -84

42, 84

Correct answer:

42, -84

Explanation:

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

Therefore, we will create two separate equations to solve.

Equation1:

$\frac{x}{7}+3 =9$

Subtract on both sides and then multiply on both sides to get x=42 .

Equation2:

$-(\frac{x}{7}+3)=9$

By distributing the negative sign, we have: $-\frac{x}{7}-3=9$ . Add to both sides and multiply both sides by , we get x=-84 .

Therefore, the solutions are,

x=42, -84 .

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Example Question #41 : How To Solve Absolute Value Equations

Solve.

$\left | 2x-3\right |-7=0$

Possible Answers:

$x=3\ \text{or}\ x=-5$

$x=-2\ \text{or}\ x=5$

$x=-5\ \text{or}\ x=5$

No solution

$x=-1\ \text{or}\ x=-5$

Correct answer:

$x=-2\ \text{or}\ x=5$

Explanation:

$\left | 2x-3\right |-7=0$

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

$(2x-3)=7\ \text{or} -(2x-3)=7$

$2x=7+3\ \text{or}\ 2x=-7+3$

$2x=10\ \text{or}\ 2x=-4$

$x=5\ \text{or}\ x=-2$

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Example Question #50 : How To Solve Absolute Value Equations

Solve for :

$\left | x+7\right |=7$

Possible Answers:

Correct answer:

Explanation:

We define the absolute value of a number as that number's distance from on the number line. Given $\left | x+7\right |=7$ , we therefore must solve for two possibilities:

1.) x+7=7 , or

2.) x+7=-7

Solving #1, we get:

x+7=7

x=0

Solving #2, we get:

x+7=-7

x=-14

Consequently, the solution is x=0 or x=-14 .

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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 #41 : How To Solve Absolute Value Equations

Example Question #42 : How To Solve Absolute Value Equations

Example Question #43 : How To Solve Absolute Value Equations

Example Question #44 : How To Solve Absolute Value Equations

Example Question #45 : How To Solve Absolute Value Equations

Example Question #46 : How To Solve Absolute Value Equations

Example Question #47 : How To Solve Absolute Value Equations

Example Question #41 : How To Solve Absolute Value Equations

Example Question #41 : How To Solve Absolute Value Equations

Example Question #50 : How To Solve Absolute Value Equations

All Algebra 1 Resources

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