Absolute Value Equations Worksheet

Absolute Value Equations Worksheet
  • Page 1
 1.  
Find the values of x, if |x| = 4.
a.
-4
b.
4, 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 |2x + 5| = 4?
a.
1 2, 9 2
b.
- 1 2, 9 2
c.
- 1 2, - 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 |5x| = 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)

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