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.

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| = x^{2}

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| = |x^{2} -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.

|x^{2} + 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| < |x^{2} + 2x + 2|

a: (-infinity , +infinity)

b: (-1 , +infinity)

c: (-infinity , -1)

d: no solutions

e: (-1 ,1)

More Problems - Applet

1 - click on the button above "click here to start" and MAXIMIZE the window obtained.

2 - click "start" on the main menu.

3 - answer the question by checking a,b,c,d or e in the lower part of the
window (maximize the window).

You can review your answers and change them by checking the desired letter.
Once you have finished, press "finish" and you get a table with your answers and the right answers to compare with.

To start another set of problems, press "reset".

Related references and links to absolute value functions and equations.