# Absolute Value Equations Worksheet

Absolute Value Equations Worksheet
• Page 1
1.
Find the values of $x$, if |$x$| = 4.
 a. -4 b. 4, $\frac{1}{4}$ c. 4 d. 4, - 4

#### Solution:

|x| = 4
[Original equation.]

The numbers that are 4 units from zero are 4 and -4.

The solutions of the equation are 4 and - 4

Correct answer : (4)
2.
What are the values of $x$, if |2$x$ + 5| = 4?
 a. $\frac{1}{2}$, $\frac{9}{2}$ b. - $\frac{1}{2}$, $\frac{9}{2}$ c. - $\frac{1}{2}$, - $\frac{9}{2}$ d. None of the above

#### Solution:

As, |2x + 5| = 4, then the values of the expression 2x + 5 is equal to 4 or -4.

2x + 5 = 4 or 2x + 5 = -4

2x + 5 - 5 = 4 - 5 or 2x + 5 - 5 = -4 - 5
[Subtract 5 from each side.]

2x = -1 or 2x = -9
[Simplify.]

x = - 1 / 2 or x = - 9 / 2
[Divide by 2 on each side.]

The solutions of the equation are - 1 / 2 and - 9 / 2.

Correct answer : (3)
3.
What are the values of $x$, if |$x$ - 6| - 3 = - 0.23?
 a. 8.77, 2.23 b. 7.77, 2.23 c. 8.77, 3.23 d. 7.77, 3.23

#### Solution:

|x - 6| - 3 = - 0.23
[Original equation.]

|x - 6| - 3 + 3 = - 0.23 + 3
[Add 3 on both sides.]

|x - 6| = 2.77
[Simplify.]

|x - 6| = 2.77, then x - 6 equals 2.77 or -2.77

x - 6 = 2.77 or x - 6 = - 2.77

x - 6 + 6 = 2.77 + 6 or x - 6 + 6 = - 2.77 + 6
[Add 6 on both sides.]

x = 8.77 or x = 3.23
[Simplify.]

The solutions of the equation are 8.77 and 3.23.

Correct answer : (3)
4.
(- |$x$|)2 is always positive. State whether the statement is true or false.
 a. True b. False

#### Solution:

The value of - |x| is always negative.

The square of a negative number is always a positive number.

So, the statement is true.

Correct answer : (1)
5.
Find the values of $x$, if |5$x$| = 0.8.
 a. 0.01, -0.01 b. 0.16, -0.16 c. 1.60, -1.60 d. 1.16, -1.16

#### Solution:

|5x| = 0.8
[Original equation.]

As, |5x| = 0.8 then the values of the expressions 5x equals to 0.8 or - 0.8

5x = 0.8 or 5x = - 0.8

x = 0.16 or x = - 0.16
[Divide by 5 on both sides.]

The solutions of the equation are 0.16 and - 0.16.

Correct answer : (2)
6.
Find the number of solutions the equation |$x$ + 3| = 0 has.
 a. 1 b. 2 c. 3

#### Solution:

The equation is |x + 3| = 0

x + 3 = 0.

x + 3 - 3 = 0 - 3.
[Subtract 3 to each side.]

x = -3

The equation has one solution.

Correct answer : (1)
7.
Find the values of $x$ in the equation |$x$| = (0.04 × 0.4).
 a. 0.016, - 0.016 b. 0.016, 0.016 c. 1.016, - 1.016

#### Solution:

|x| = (0.04 x 0.4)
[Original equation.]

|x| = 0.016
[Simplify.]

The numbers that are 0.016 units from zero are 0.016 and - 0.016;.

The values of x are 0.016 and -0.016.

Correct answer : (1)
8.
"The value of -|$s$| is always positive." Determine whether the statement is true or false.
 a. True b. False

#### Solution:

The value of |s| is always positive.

But the value of -|s| is always negative.

So, the statement is false.

Correct answer : (2)
9.
Solve the equation |$x$| = 5.
 a. 5 , - 5 b. - 5 , - 5 c. 5 , 5 d. 5 , 0

#### Solution:

|x| = 5
[Original eqution.]

The numbers that are 5 units from zero are 5 and - 5.

So, there are two solutions 5 and - 5.

Correct answer : (1)
10.
Solve the equation |$x$| = 5.5.
 a. 0, - 5.5 b. - 5.5, - 5.5 c. 5.5, 5.5 d. 5.5, - 5.5

#### Solution:

|x| = 5.5

The numbers that are 5.5 units from zero are 5.5, - 5.5.

There are two solutions, which are 5.5 and - 5.5.

Correct answer : (4)

*AP and SAT are registered trademarks of the College Board.