Question

Solve the absolute value inequality: |2x - 3| < 5

x < -1 and x > 4

x > -1 and x < 4

x < -1 or x > 4

x > -4 and x < 4

Answer 1

Where is the graph?

Answer 2

you have two equations.
2x - 3 < 5
and
-(2x-3) < 5
or simply..
2x - 3 > - 5

Answer 3

Just solve for x.

Answer 4

If \[|x| < y\] then \[-y < x < y\]

Therefore, \[|2x-3| < 5\]\[= -5 < 2x-3 < 5\]
Now solve for x.

Answer 5

how

Answer 6

Isolate it.
First you're going to add 3 to all sides of the inequality to remove the -3 from the center.
\[-5+3 < 2x-3+3 < 5+3\]\[=-2<2x<8\]Now you have to divide both sides by 2.
\[\frac{-2}{2} < \frac{2x}{2} < \frac{8}{2}\]\[=-1<x<4\]
Therefore, \[x > -1\] and \[x < 4\]