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Algebra II : Absolute Value

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Example Questions

Example Question #2 : Absolute Value Inequalities

Solve the inequality.

$\small \left | x+2 \right |>5$

Possible Answers:

$\small x<-3\ or\ x>7$

$\small x<-7\ or\ x>3$

$\small -7<x<3$

$\small -3<x<7$

Correct answer:

$\small x<-7\ or\ x>3$

Explanation:

$\small \left | x+2 \right |>5$

Remove the absolute value by setting the term equal to either $\small 5$ or $\small -5$ . Remember to flip the inequality for the negative term!

$\small x+2>5\ or\ x+2<-5$

Solve each scenario independently by subtracting $\small 2$ from both sides.

$\small x+2-2>5-2\ or\ x+2-2<-5-2$

$\small x>3\ or\ x<-7$

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Example Question #6 : Absolute Value Inequalities

Solve for :

| 4y + 7 | > -5

Possible Answers:

$(-\infty , \infty )$

$\left(-\infty , -\frac{1}{2}\right) \cup \left ( \frac{1}{2}, \infty \right)$

$\left(-\infty , -\frac{1}{2}\right) \cup \left (3, \infty \right)$

$(-\infty , -3) \cup \left ( \frac{1}{2}, \infty \right)$

$(-\infty , -3) \cup (3, \infty )$

Correct answer:

$(-\infty , \infty )$

Explanation:

The absolute value of any number is nonnegative, so | 4y + 7 | must always be greater than . Therefore, any value of makes this a true statement.

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Example Question #11 : Absolute Value

Solve for .

$x+5=\left | 7\right |$

Possible Answers:

2, -12

Correct answer:

2, -12

Explanation:

When solving for absolute values, remember there's an equation for positive value and another equation for negative value.

x+5=7, x+5=-7 . S

ubtract on both sides of all equations.

x=2, x=-12

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Example Question #12 : Solving Absolute Value Equations

Solve for .

$x-6=\left | 2\right |$

Possible Answers:

-4, -8

4, 8

-2, -6

Correct answer:

4, 8

Explanation:

When solving for absolute values, remember there's an equation for positive value and another equation for negative value.

x-6=2, x-6=-2

Add to both sides of both equations.

x=4, x=8

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Example Question #12 : Absolute Value

Solve for .

$\frac{x}{5}=\left | 3\right |$

Possible Answers:

-5, 5

15, -15

Correct answer:

15, -15

Explanation:

When solving for absolute values, remember there's an equation for positive value and another equation for negative value.

$\frac{x}{5}=3, \frac{x}{5}=-3$

Multiply both sides by for both equations.

x=15, x=-15

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Example Question #11 : Absolute Value

Solve for .

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

Possible Answers:

$\frac{3}{7}$

$\pm \frac{3}{7}$

$\pm \frac{7}{3}$

$\frac{7}{3}$

$-\frac{3}{7}$

Correct answer:

$\pm \frac{3}{7}$

Explanation:

When solving for absolute values, remember there's an equation for positive value and another equation for negative value.

7x=3, 7x=-3

Divide both sides by for both equations.

$x=\pm \frac{3}{7}$

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Example Question #12 : Absolute Value

Solve:

$\left | 2x-1 \right |=13$

Possible Answers:

x=7, 6

x=-6

x=7,-6

x=7

x=-7,-6

Correct answer:

x=7,-6

Explanation:

To solve absolute value equations, you have to set up the equation two different ways to account for two answers.

The first is how you see it:

2x-1=13 .

The second is by making the answer negative:

2x-1=-13 .

Next solve each one for x. The first equation yields x to be 7. The second one gives you x=-6. Those are your two answers.

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Example Question #15 : Solving Absolute Value Equations

Solve for :

$\left | x-5\right |+8<3$

Possible Answers:

$x<-6 \and\ x>16$

$x<0 \and\ x>10$

No solution

x<0

Correct answer:

No solution

Explanation:

Given

$\left | x-5\right |+8<3$

first subtract 8 from both sides to get on the right.

$\left | x-5\right |<-5$

Based upon what we know about absolute value functions, it is impossible for an absolute value to be negative. So it is also impossible for an absolute value to be less than a negative number, which in this case is (-5) .

The only answer can be No Solution.

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Example Question #12 : Absolute Value

Solve for :

$2 \left | 3x-1 \right | = 10$

Possible Answers:

1.5; -1.5

2; -2

2; 1.5

$2; -\frac{4}{3}$

1;0

Correct answer:

$2; -\frac{4}{3}$

Explanation:

Solve using inverse opperations:

$2 \left | 3x-1 \right | = 10$

Divide both sides by 2.

|3x - 1 | = 5

Because the absolute value function always makes whatever is inside positive, this gives us two solutions. 3x - 1 could be either or , so we'll solve for both:

3 x - 1 = 5

3x = 6

x = 2

3x - 1 = -5

3x = -4

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

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Example Question #12 : Absolute Value

Solve for :

|2x - 7 | - 4 = 9

Possible Answers:

-1; 1

10; -10

10; 1

10; -3

-3; 1

Correct answer:

10; -3

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

|2x - 7 | - 4 = 9

First add 4 to both sides

|2x - 7 | = 13

The absolute value function makes whatever is inside positive, which means that there are two possible solutions. 2x - 7 could either be or
so we'll solve for both

2x - 7 = 13

2 x = 20

x = 10

2 x - 7 = -13

2x = -6

x = -3

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Algebra II : Absolute Value

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2 : Absolute Value Inequalities

Example Question #6 : Absolute Value Inequalities

Example Question #11 : Absolute Value

Example Question #12 : Solving Absolute Value Equations

Example Question #12 : Absolute Value

Example Question #11 : Absolute Value

Example Question #12 : Absolute Value

Example Question #15 : Solving Absolute Value Equations

Example Question #12 : Absolute Value

Example Question #12 : Absolute Value

All Algebra II Resources

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