Absolute Value Inequalities

Find the solutions of the inequality

$\begin{displaymath}\vert x+2\vert\leq 3.\end{displaymath}$

To use our distance terminology, we have to change the inequality to

$\begin{displaymath}\vert x-(-2)\vert\leq 3.\end{displaymath}$

We want to find all real numbers x whose distance to -2 does not exceed 3. We are talking about the numbers in the interval [-5,1].

1998-06-08