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Absolute Value Function Worksheet

Absolute Value Function Worksheet
  • Page 1
 1.  
Solve: |5 - 9x| - 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.


Correct answer : (3)
 2.  
Find the values of x, if |5x| = 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.


Correct answer : (3)
 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.


Correct answer : (4)
 4.  
How many solutions does the equation |x| - 1 = 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.


Correct answer : (2)
 5.  
What are the values of x, if |5x + 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.


Correct answer : (2)
 6.  
Find the values of x, if |x| = 3.
a.
-3
b.
3
c.
3, - 3
d.
3, 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.


Correct answer : (3)
 7.  
What are the values of x, if |4x + 9| = 8?
a.
- 1 4, - 1 4
b.
- 1 4, 17 4
c.
1 4, 17 4
d.
- 1 4, - 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.


Correct answer : (4)
 8.  
What are the values of x, if |x| = -2 3?
a.
2 3, -2 3
b.
No Solution
c.
2 3, 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.


Correct answer : (2)
 9.  
Find the values of x, if |x - 2| = 3 5.
a.
13, 7
b.
13 5 , 7 5
c.
13 5 , - 7 5
d.
- 13 5 , 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.]


Correct answer : (2)
 10.  
Find the values of x, if |4x - 5| = 10.
a.
-15 4, -5 4
b.
15, -5
c.
15 4, -5 4
d.
-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.


Correct answer : (3)

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