solve |4x-3|<8

I'd just do it like this (this is easier)   :)

$$\\ |4x-3|<8\\\\
-8<4x-3<8\\\\
$add 3 to all 3 'sides'$\\\\
-8+3<4x-3+3<8+3\\\\
-5<4x<11\\\\
\frac{-5}{4}

This graph might help:

.

Here's another graph......https://www.desmos.com/calculator/wl6arl5s0g

Notice that the values that make the inequality true occur on (-1.75, 2.75)