# Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 137: 6

$\{x\ |\ \ -2 \leq x \leq 5\ \}$

#### Work Step by Step

Recall the general rules for writing intervals: An interval may be annotated as $[a,b],\ (a,b],\ [a,b),\ (a,b),\ (-\infty,b],\ (-\infty,b),\ [a,\infty),\ (a,\infty).$ It contains numbers between the left and right borders. The inequality signs depend on whether a border is included in the set or not. The bracket "[", or "]" means "border included" and the sign is "$\leq$". The parenthesis "(" or ")" means "border excluded" and the sign is "$\lt$". $\pm\infty$ implies "no border", so it is always accompanied by a parenthesis. For example $[a,b)=\{x\ |\ a\leq x\lt b\ \}$ $(-6,\infty)=\{x\ |\ x\gt-6\ \}$ $(-\infty,3]=\{x\ |\ \ x\leq 3\ \}$ --- Here, both borders are included, so: $[-2,5]$ = $\{x\ |\ \ -2 \leq x \leq 5\ \}$

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