# Absolute Value Function Worksheet

Absolute Value Function Worksheet
• Page 1
1.
Solve: |5 - 9$x$| - 4 = 28
 a. 3, -4.11 b. 3, 4.11 c. -3, 4.11 d. -3, -4.11

#### Solution:

|5 - 9x| - 4 = 28

|5 - 9x| - 4 + 4 = 28 + 4
[Add 4 to both sides of the equation.]

|5 - 9x| = 32
[Simplify.]

5 - 9x = 32 or 5 - 9x = - 32
[The expression 5 - 9x is equal to 32 or - 32.]

- 9x = 32 - 5 or - 9x = - 32 - 5
[Subtracting 5 from the two sides of the equation.]

- 9x = 27 or - 9x = -37
[Simplify.]

x = -3 or x = 4.11
[Divide throughout by - 9.]

The solutions for the equation are -3 and 4.11.

2.
Find the values of $x$, if |5$x$| = 0.1.
 a. 1.02, - 1.02 b. 0.00, - 0.00 c. 0.02, - 0.02 d. 0.20, - 0.20

#### Solution:

|5x| = 0.1

As, |5x| = 0.1 then the values of the expressions 5x equals to 0.1 or - 0.1

5x = 0.1 or 5x = - 0.1

x = 0.02 or x = - 0.02
[Divide throughout by 5.]

The solutions of the equation are 0.02 and - 0.02.

3.
Find the values of $x$, if |$x$ - 3| = 6.
 a. -3 , -1 b. -3, 6 c. 9, - 9 d. 9, -3

#### Solution:

|x - 3| = 6

x - 3 = 6 or x - 3 = - 6
[Removing the modulus.]

x - 3 + 3 = 6 + 3 or x - 3 + 3 = - 6 + 3
[Add 3 to both sides of the equation.]

x = 9 or x = -3
[Simplify.]

The solutions of the equation are 9 and -3.

4.
How many solutions does the equation |$x$| - 1 = $\frac{5}{4}$ have?
 a. 1 b. 2 c. 3

#### Solution:

|x| - 1 = 5 / 4

|x| - 1 + 1 = 5 / 4 + 1
[Add 1 to both sides of the equation.]

|x| = 9 / 4
[Simplify.]

|x| = 9 / 4, then x = 9 / 4and x = - 9 / 4.

The solutions of the equation are 9 / 4 and - 9 / 4 .

So, there are two solutions for the equation.

5.
What are the values of $x$, if |5$x$ + 3| = 0.4?
 a. 0.52, -0.68 b. -0.52, -0.68 c. 0.52, 0.68 d. -0.52, 0.68

#### Solution:

|5x + 3| = 0.4, the expression 5x + 3 is equal to -0.4 or 0.4.

5x + 3 = 0.4 or 5x + 3 = -0.4.

5x + 3 - 3 = 0.4 - 3 or 5x + 3 - 3 = -0.4 - 3
[Subtracting 3 from the two sides of the equation.]

5x = -2.6 or 5x = -3.4
[Simplify.]

x = -0.52 or x = -0.68
[Divide throughout by 5.]

There are two solutions for the expression, which are -0.52 and -0.68.

6.
Find the values of $x$, if |$x$| = 3.
 a. -3 b. 3 c. 3, - 3 d. 3, $\frac{1}{3}$

#### Solution:

|x| = 3

The numbers that are 3 units from zero are 3 and -3.

The solutions of the equation are 3 and - 3.

7.
What are the values of $x$, if |4$x$ + 9| = 8?
 a. - $\frac{1}{4}$, - $\frac{1}{4}$ b. - $\frac{1}{4}$, $\frac{17}{4}$ c. $\frac{1}{4}$, $\frac{17}{4}$ d. - $\frac{1}{4}$, - $\frac{17}{4}$

#### Solution:

As, |4x + 9| = 8, then the values of the expression 4x + 9 is equal to 8 or -8.

4x + 9 = 8 or 4x + 9 = -8

4x + 9 - 9 = 8 - 9 or 4x + 9 - 9 = -8 - 9
[Subtracting 9 from the two sides of the equation.]

4x = -1 or 4x = -17
[Simplify.]

x = - 1 / 4 or x = - 17 / 4
[Divide throughout by 4.]

The solutions of the equation are - 1 / 4 and - 17 / 4.

8.
What are the values of $x$, if |$x$| = $\frac{-2}{3}$?
 a. $\frac{2}{3}$, -$\frac{2}{3}$ b. No Solution c. $\frac{2}{3}$, $\frac{2}{3}$ d. None of the above

#### Solution:

|x| = - 23

The absolute value of a positive or a negative number is always a positive number.

The equation has no solution.

9.
Find the values of $x$, if |$x$ - 2| = $\frac{3}{5}$.
 a. 13, 7 b. $\frac{13}{5}$ , $\frac{7}{5}$ c. $\frac{13}{5}$ , - $\frac{7}{5}$ d. - $\frac{13}{5}$ , $\frac{7}{5}$

#### Solution:

| x - 2| = 3 / 5

The expression x - 2 is equal to 3 / 5or - 3 / 5.

x - 2 = 3 / 5 or x - 2 = - 3 / 5

x - 2 + 2 = 3 / 5 + 2 or x - 2 + 2 = - 3 / 5 + 2
[Add 2 to both sides of the equation.]

The solutions of the equation are 13 / 5 and 7 / 5.
[Simplify.]

10.
Find the values of $x$, if |4$x$ - 5| = 10.
 a. $\frac{-15}{4}$, $\frac{-5}{4}$ b. 15, -5 c. $\frac{15}{4}$, $\frac{-5}{4}$ d. $\frac{-5}{2}$, 15

#### Solution:

|4x - 5| = 10

4x - 5 = 10 or 4x - 5 = - 10
[The expression 4x - 5 is equal to 10 and - 10.]

4x - 5 + 5 = 10 + 5 or 4x - 5 + 5 = - 10 + 5
[Add 5 to both sides of the equation.]

4x = 15 or 4x = -5
[Simplify.]

x = 154 or x = -54
[Divide throughout by 4.]

The equation has two solutions 15 / 4 and -5 / 4.