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Absolute Value Equations Worksheet
Practice Problems
x
[Original equation.]
The numbers that are 4 units from zero are 4 and -4.
The solutions of the equation are 4 and - 4
x x
2x x
2x x
[Subtract 5 from each side.]
2x x
[Simplify.]
x 1 2 x 9 2
[Divide by 2 on each side.]
The solutions of the equation are -1 2 9 2
x
[Original equation.]
|x
[Add 3 on both sides.]
|x
[Simplify.]
|x x or
x x
x x
[Add 6 on both sides.]
x x
[Simplify.]
The solutions of the equation are 8.77 and 3.23.
(- ||)2 is always positive. State whether the statement is true or false.
x
The square of a negative number is always a positive number.
So, the statement is true.
x
[Original equation.]
As, |5x x
5x x
x x
[Divide by 5 on both sides.]
The solutions of the equation are 0.16 and - 0.16.
x
x
x
[Subtract 3 to each side.]
x
The equation has one solution.
x
[Original equation.]
|x
[Simplify.]
The numbers that are 0.016 units from zero are 0.016 and - 0.016;.
The values ofx
s
But the value of -|s
So, the statement is false.
x
[Original eqution.]
The numbers that are 5 units from zero are 5 and - 5.
So, there are two solutions 5 and - 5.
x
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.
Absolute Value Equations Worksheet
- Page 1
1.
Find the values of , if || = 4.
| a. | -4 | ||
| b. | 4, | ||
| c. | 4 | ||
 | d. | 4, - 4 |
Solution:
|[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 , if |2 + 5| = 4?
| a. | , | ||
| b. | - , | ||
| c. | - , - | |
| d. | None of the above |
Solution:
As, |22
2
[Subtract 5 from each side.]
2
[Simplify.]
[Divide by 2 on each side.]
The solutions of the equation are -
Correct answer : (3)
3.
What are the values of , if | - 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:
|[Original equation.]
|
[Add 3 on both sides.]
|
[Simplify.]
|
[Add 6 on both sides.]
[Simplify.]
The solutions of the equation are 8.77 and 3.23.
Correct answer : (3)
4.
| a. | True | |
| b. | False |
Solution:
The value of - |The square of a negative number is always a positive number.
So, the statement is true.
Correct answer : (1)
5.
Find the values of , if |5| = 0.8.
| a. | 0.01, -0.01 | ||
| b. | 0.16, -0.16 | |
| c. | 1.60, -1.60 | ||
| d. | 1.16, -1.16 |
Solution:
|5[Original equation.]
As, |5
5
[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 | + 3| = 0 has.
| a. | 1 | |
| b. | 2 | ||
| c. | 3 |
Solution:
The equation is |[Subtract 3 to each side.]
The equation has one solution.
Correct answer : (1)
7.
Find the values of in the equation || = (0.04 × 0.4).
| a. | 0.016, - 0.016 | |
| b. | 0.016, 0.016 | ||
| c. | 1.016, - 1.016 |
Solution:
|[Original equation.]
|
[Simplify.]
The numbers that are 0.016 units from zero are 0.016 and - 0.016;.
The values of
Correct answer : (1)
8.
"The value of -|| is always positive." Determine whether the statement is true or false.
| a. | True | ||
| b. | False |
Solution:
The value of |But the value of -|
So, the statement is false.
Correct answer : (2)
9.
Solve the equation || = 5.
| a. | 5 , - 5 | |
| b. | - 5 , - 5 | ||
| c. | 5 , 5 | ||
| d. | 5 , 0 |
Solution:
|[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 || = 5.5.
| a. | 0, - 5.5 | ||
| b. | - 5.5, - 5.5 | ||
| c. | 5.5, 5.5 | ||
| d. | 5.5, - 5.5 |
Solution:
|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)