Equations And Inequalities with Absolute Value - Problems

A set of 10 multiple choice problems related to equations and inequalities with absolute value and their answers problems are presented. The same problems can also be solved as a self test using an applet.

You may want to work through the tutorials:
Solve Inequalities With Absolute Value - Tutorials and Solve Equations with absolute value before you start the self test.

Problems with answers

For each problem, select the correct answer.

Problem 1: Find all real solutions to the equation with absolute value.

2|-2x - 2| - 3 = 13


a: -5

b: 3

c: -5 , 3

d: no solutions

e: 0

Problem 2: Find all real solutions to the equation with absolute value.

|x - 1| = 2x + 1


a: -2

b: -2 , 0

c: -1

d: no solutions

e: 0

Problem 3: Find all real solutions to the equation with absolute value.

|2x - 1| = x2


a: -1 - sqrt(2) , -1 + sqrt(2) , 1

b: 1

c: -1 , 1

d: -1 - sqrt(2) , -1 + sqrt(2)

e: no solutions

Problem 4: Find all real solutions to the equation with absolute value.

-2|x + 1| -2 = 4


a: -4

b: no solutions

c: 4

d: all real numbers

e: 0

Problem 5: Find all real solutions to the equation with absolute value.

|x - 1| = |x2 -2x + 1|


a: no solutions

b: 0

c: 3

d: 0 , 1 , 2

e: 2 + sqrt(2) , 2 - sqrt(2)

Problem 6: Solve the inequality with absolute value..

|x - 1| >= 2


a: no solutions

b: [3 , +infinity)

c: (-infinity , -1] U [3 , +infinity)

d: (-infinity , -1]

e: (-infinity , +infinity)

Problem 7: Solve the inequality with absolute value..

-3|-2x + 4| <= 4


a: (-infinity , 7/3)

b: (7/3 , +infinity)

c: (-7/3 , +7/3)

d: (0 , 7/3)

e: (-infinity , +infinity)

Problem 8: Solve the inequality with absolute value..

|3x + 1| <= 2x + 3


a: [-4/5 , 2]

b: (-infinity , +infinity)

c: no solutions

d: all real numbers

e: [-4/5 , +infinity)

Problem 9: Solve the inequality with absolute value.

|x2 + x - 2| < x + 3


a: (-sqrt(5), sqrt(5))

b: no solutions

c: (-sqrt(5), -1) U (-1 , sqrt(5))

d: (-infinity, -1) U (-1 , +infinity)

e: (-1 , sqrt(5))

Problem 10: Solve the inequality with absolute values.

|x + 1| < |x2 + 2x + 2|


a: (-infinity , +infinity)

b: (-1 , +infinity)

c: (-infinity , -1)

d: no solutions

e: (-1 ,1)

More Problems - Applet



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Related references and links to absolute value functions and equations.


Math Problems, Questions and Online Self Tests.

Solve Inequalities With Absolute Value - Tutorials.

Solve Equations with Absolute Value.

Absolute Value Functions.

Definition of the Absolute Value Function.

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