Question

please help me!
Part 1: Solve |4x-11| < 5. You must show all work.

Part 2: Use complete sentences to describe the graph in words

Answer 1

|4x-11| < 5 means either 4x - 11 < 5 or 4x - 11 > -5

First,
4x - 11 < 5
4x - 11 + 11 < 5 + 11
4x < 16
4x/4 < 16/4
x < 4

Second,
4x - 11 > -5
4x - 11 + 11 > -5 + 11
4x > 6
4x/4 > 6/4
x > 3/2

Third, is to graph these solutions on a number line and check to make sure they do not contradict each other or the original equation.