SOLVING EQUATIONS WITH ABSOLUTE VALUES ON BOTH SIDES WORKSHEET

Solve the following absolute value equations.

Problem 1 :

|x + 4| = |2x - 7|

Solution

Problem 2 :

|3x + 5| = |x - 6|

Solution

Problem 3 :

|x - 9| = |x + 6|

Solution

Problem 4:

|x + 4| = |x - 3|

Solution

Problem 5 :

|5t + 7| = |4t + 3|

Solution

Problem 6 :

|3a - 1| = |2a + 4|

Solution

Problem 7 :

|n - 3| = |3 - n|

Solution

Problem 8 :

|y - 2| = |2 - y|

Solution

Problem 9 :

|7 - a| = |a + 5|

Solution

Problem 10 :

|6 - t| = |t + 7|

Solution

Problem 11 :

|1/2x - 5| = |1/4x + 3|

Solution

Problem 1 :

Solve for x :

|(3x + 2)/(1 – x)| = 4

Solution

Problem 2 :

Solve for x :

|x /(x – 1)| = 3

Solution

Problem 3 :

Solve for x :

|(2x - 1)/(x + 1)| = 5

Solution

Problem 4 :

Solve for x :

|(x + 3)/(1 – 3x)| = 1/2

Solution

Problem 5 :

Solve for x :

|x/(x – 2)| = 3

Solution

Problem 6 :

Solve for x :

|(2x + 3)/(x – 1)| = 2

Solution

Write the solution set of each equation.

Problem 1 :

│x - 5│ = 12

Solution

Problem 2 :

│x + 8│ = 6

Solution

Problem 3 :

│2a - 5│ = 7

Solution

Problem 4 :

│5b - 10│ = 25

Solution

Problem 5 :

│3x - 12│ = 9

Solution

Problem 6 :

│4y + 2│ = 14

Solution

Problem 7 :

│35 - 5x│ = 10

Solution

Problem 8 :

│-5a│+ 7 = 22

Solution

Problem 9 :

│8 + 2b│ - 3 = 9

Solution

Problem 10 :

│2x - 5│ + 2 = 13

Solution

Problem 11 :

│4x - 12│ + 8 = 0

Solution

Problem 12 :

│7 - x│ + 2 = 12

Solution

Problem 13 :

In a cheer leading competition, the minimum length of a routine is 4 minutes. The maximum length of a routine is 5 minutes. Write an absolute value equation that represents the minimum and maximum lengths

Solution

Problem 14 :

The minimum distance from Earth to the Sun is 91.4 million miles. The maximum distance is 94.5 million miles.

a. Represent these two distances on a number line.

b. Write an absolute value equation that represents the minimum and maximum distances.

Solution

Problem 15 :

Match the absolute value equation with its graph without solving the equation.

a) ∣ x + 2 ∣ = 4

b) ∣ x − 4 ∣ = 2

c)  ∣ x − 2 ∣ = 4

d) ∣ x + 4 ∣ = 2

Solution

Answer Key

1) x = 17 (or) x = -7

2) x = -2 (or) x = -14

3) a = 6 (or) a = -1

4) b = 7 (or) b = -3

5) x = 7 (or) x = 1

6) y = 3 (or) y = -4

7) x = 5 (or) x = 9

8) a = -3 (or) a = 3

9) b = 2 (or) b = -10

10) x = 8 (or) x = -3

11) Absolute value cannot be less than 0. So there is no solution.

12) x = -3 (or) x = 17

13) |x - 4.5| = 0.5

14) 

15) a) Option B

b) Option D

c) Option C

d) Option A

Problem 1 :

|x – 1| = 5x + 10

Solution

Problem 2 :

|2z – 3| = 4z - 1

Solution

Problem 3 :

|3x + 5| = 5x + 2

Solution

Problem 4 :

|2y – 4| = 12

Solution

Problem 5 :

3|4w – 1| - 5 = 10

Solution

Problem 6 :

|2x + 5| = 3x + 4

Solution

Problem 7 :

You are driving on a highway and are about 250 miles from your state’s border. You set your cruise control at 60 miles per hour and plan to turn it off within 30 miles of the border on either side. Find the minimum and maximum numbers of hours you will have cruise control on.

Solution