Question

Is it true that without making a graph of an absolute value function, you can describe its position in the coordinate plane? Explain with an example.

Answer 1

For example:

$$
|2x +3| < 7\\
\implies -7 < 2x+3 < 7\\
\implies -7-3< 2x < 7-3\\
\implies -10<2x<4\\
\implies \cfrac{-10}{2}<\cfrac{2x}{2}<\cfrac{4}{2}\\
\implies -5<x<2
$$
Which describes an absolute value functions without a graph:

Just take all values of \(x\) that are between -5 and 2.