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| = 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.
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. |