Solve simple Absolute Value Inequality

 Exam - BARTON COLLEGE PRACTICE PLACEMENT TEST Ex. 39

Exercise:

The inequality |8 - x| < 8   is equivalent to:

 
a) x < 0

b) x > 0

c) x<0 or x > 16

d) 0 < x < 16

 Solution

Solve the absolute value inequality:  |8 - x| < 8

We solve the inequality 8-x < 8 and the inequality -(8-x) < 8, and than find intersection between the solutions.

Solution 1 for  (8-x) >=0
8 - x < 8
8 - 8 < x
x > 0 

 

x > 0 and (8-x) >=0 is:

0 < x <= 8

Solution 2 for (8-x) <=0
-(8-x) < 8
-8 + x < 8
x < 8 + 8

x < 16

 

x <16 and (8-x) <=0 is  8 <= x < 16

The combination of solution 1 and 2 : 

 0 < x <= 8 OR   8 <= x < 16  is

 

0 < x < 16

The correct solution is d.

We can see the problem graphicaly:

 The inequality |8 - x| < 8   is equivalent to  0 < x < 16