SOLVING ABSOLUTE VALUE EQUATIONS WORKSHEET PDF

Solving Absolute Value Equations Worksheet Pdf :

Worksheet given in this section will be much useful for the students who would like to practice problems on solving absolute value equations. 

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Solving Absolute Value Equations Worksheet - Problems

Problem 1 :

Solve the absolute value equation :

|3x + 5|  =  7

Problem 2 : 

Solve the absolute value equation :

|7x|  =  21

Problem 3 :

Solve the absolute value equation :

|2x + 5| + 6  =  7

Problem 4 :

Solve the absolute value equation : 

|x - 3| + 6  =  6

Problem 5 :

Solve the absolute value equation :

2|3x +4|  =  7

Problem 6 :

Solve the absolute value equation :

3|5x - 6| - 4  =  5

Problem 7 :

Solve the absolute value equation :

|x² - 4x - 5| = 7

Problem 8 :

Solve the absolute value equation :

0.5|0.5x| - 0.5  =  2.5

Problem 9 :

If the absolute value equation |2x + k|  =  3 has the solution x  =  -2, find the value of k. 

Problem 10 :

If the absolute value equation |x - 3| - k = 0 has the solution x  =  -5, find the value of k. 

Solving Absolute Value Equations Worksheet - Solutions

Problem 1 :

Solve the absolute value equation :

|3x + 5|  =  7

Solution :

Solve :

|3x + 5|  =  7

3x + 5  =  7     or     3x + 5  =  -7 

3x  =  2     or     3x  =  -12

x  =  2/3     or     x  =  -4

Hence the solution is x  =  -4, 2/3.

Problem 2 : 

Solve the absolute value equation :

|7x|  =  21

Solution :

Solve :

|7x|  =  21

7x  =  21     or     7x  =  -21 

x  =  3     or     x  =  -3

Hence, the solution is x  =  -3, 3

Problem 3 :

Solve the absolute value equation :

|2x + 5| + 6  =  7

Solution :

Solve :        

|2x + 5| + 6  =  7

Subtract 6 from each side.

|2x + 5|  =  1

2x + 5  =  1     or     2x + 5  =  1 

2x  =  -4     or     2x  =  -6

x  =  -2     or     x  =  -3

Hence, the solution is x  =  -2, -3.

Problem 4 :

Solve the absolute value equation : 

|x - 3| + 6  =  6

Solution :

Solve :        

|x - 3| + 6  =  6

Subtract 6 from each side.

|x - 3| + 6  =  6

Subtract 6 from each side.

|x - 3|  =  0

x - 3  =  0     or     x - 3  =  0 

x  =  3     or     x  =  3

Hence, the solution is x  =  3, 3.

Problem 5 :

Solve the absolute value equation :

2|3x +4|  =  7

Solution :

Solve :              

2|3x +4|  =  7

Divide each side by 2. 

|3x + 4|  =  7/2

3x + 4  =  7/2     or     3x + 4  =  -7/2

3x  =  7/2 - 4     or     3x  =  -7/2 - 4

3x  =  -1/2     or     3x  =  -15/2

x  =  -1/6     or     x  =  -15/6

x  =  -1/6     or     x  =  -5/2

Hence the solution is x  =  -1/6, -5/2.

Problem 6 :

Solve the absolute value equation :

3|5x - 6| - 4  =  5

Solution :

Solve : 

3|5x - 6| - 4  =  5

Add 4 to each side.

3|5x - 6|  =  9

Divide each side by 3.

|5x - 6|  =  3

5x - 6  =  3     or     5x - 6  =  -3

5x  =  9     or     5x  =  3

x  =  9/5     or     x  =  3/5

Hence the solution is x  =  9/5, 3/5.

Problem 7 :

Solve the absolute value equation :

|x² - 4x - 5| = 7

Solution :

Solve :

|x² - 4x - 5|  =  7

x² - 4x  - 5  =  7     or     x² - 4x - 5  =  -7 

x² - 4x  - 12  =  0     or     x² - 4x + 2  =  0 

Solve the first quadratic equation x² - 4x - 12  =  0.

x² - 4x  - 12  =  0

(x + 2)(x - 6)  =  0

x + 2  =  0     or     x - 6  =  0

x  =  -2     or     x  =  6 

Solve the second quadratic equation x² - 4x + 2  =  0.

This quadratic equation can not be solved using factoring. Because the left side part can not be factored.

So, we can use quadratic formula and solve the equation as shown below. 

Hence, the solution is x  =  -2, 7, 2 ± √2.

Problem 8 :

Solve the absolute value equation :

0.5|0.5x| - 0.5  =  2.5

Solution :

Solve :

0.5|0.5x| - 0.5  =  2.5

Add 0.5 to each side. 

0.5|0.5x|  =  3

Divide each side by 0.5

|0.5x|  =  6

0.5x  =  6     or     0.5x  =  -6

x  =  12     or     x  =  -12

Hence the solution is x  =  -12, 12.

Problem 9 :

If the absolute value equation |2x + k|  =  3 has the solution x  =  -2, find the value of k. 

Solution :

Because x  =  -2 is a solution, substitute x  =  -2 in the given absolute value equation. 

|2(-2) + k|  =  3

|-4 + k|  =  3

Solve for k :

-4 + k  =  3     or     -4 + k  =  -3

k  =  7     or     k  =  1

Hence, the value of k  =  1, 7.

Problem 10 :

If the absolute value equation |x - 3| - k = 0 has the solution x  =  -5, find the value of k. 

Solution :

Because x  =  -2 is a solution, substitute x  =  -2 in the given absolute value equation. 

|-5 - 3| - k  =  0

|-8| - k  =  0

8 - k  =  0

8  =  k

Hence the value of k  =  8.

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