Absolute Value Inequalities

Exercise 4.

Find the solutions of the inequality

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

Answer.

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].

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Helmut Knaust
1998-06-08

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