Answer
$\dfrac{b-c}{a} \lt x \lt \dfrac{b+c}{a}$
Work Step by Step
Consider the inequality $-c \lt ax -b \lt c$
This can also be written as: $-c+b \lt ax \lt c+b$
or, $\dfrac{-c+b}{a} \lt x \lt \dfrac{c+b}{a}$
Our result is: $\dfrac{b-c}{a} \lt x \lt \dfrac{b+c}{a}$
