What is the solution to the inequality abs(2x-1) <9|2x1|<9?

1 Answer
Aug 17, 2015

x > -4x>4 and x < 5x<5

-4 < x < 54<x<5

Explanation:

When solving an inequality with absolute value we really have
two inequalities

2x-1< 92x1<9 and -(2x-1)< 9(2x1)<9

Solving each one as follows

2x-1 < 92x1<9

2x<102x<10

x < 5x<5

Now for the next one

-(2x-1)< 9(2x1)<9

2x-1> -92x1>9 Dividing by the negative flips the inequality sign

2x > -82x>8

x > -4x>4