Equations And Inequalities with Absolute Value

Multiple choice questions on solving equations and inequalities with absolute value are presented. The answers to the questions below are included.
You may want to work through the tutorials on solving inequalities with absolute value and solving equations with absolute value before solving the questions below.



For each question, select the correct answer.
Question 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
Question 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
Question 3: Find all real solutions to the equation with absolute value.
|2x - 1| = x2

a: -1 - √2 , -1 + √2 , 1
b: 1
c: -1 , 1
d: -1 - √2 , -1 + √2
e: no solutions
Question 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
Question 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 + √2 , 2 - √2
Question 6: Solve the inequality with absolute value..
|x - 1| >= 2

a: no solutions
b: [3 , +∞)
c: (-∞ , -1] U [3 , +∞)
d: (-∞ , -1]
e: (-∞ , +∞)
Question 7: Solve the inequality with absolute value..
-3|-2x + 4| <= 4

a: (-∞ , 7/3)
b: (7/3 , +∞)
c: (-7/3 , +7/3)
d: (0 , 7/3)
e: (-∞ , +∞)
Question 8: Solve the inequality with absolute value..
|3x + 1| <= 2x + 3

a: [-4/5 , 2]
b: (-∞ , +∞)
c: no solutions
d: all real numbers
e: [-4/5 , +∞)
Question 9: Solve the inequality with absolute value.
|x2 + x - 2| < x + 3

a: (-√5, √5)
b: no solutions
c: (-√5, -1) U (-1 , √5)
d: (-∞, -1) U (-1 , +∞)
e: (-1 , √5)
Question 10: Solve the inequality with absolute values.
|x + 1| < |x2 + 2x + 2|

a: (-∞ , +∞)
b: (-1 , +∞)
c: (-∞ , -1)
d: no solutions
e: (-1 ,1)

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.