How do yu find the AV of
|x - 5| = 8
$\displaystyle |x+1|-4 \leq -1$
First, you would add 4 to both sides. You need to isolate the absolute value part of your inequality.
$\displaystyle |x+1| \leq 3$
Now, use the rule from my last post that applies.
$\displaystyle -3 \leq x+1 \leq 3$
Subtract 1 from each part of the inequality.
$\displaystyle -3 \leq x+1 \leq 3$
$\displaystyle -1 \ \ \ \ \ \ -1 -1$
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$\displaystyle -4 \leq x \leq 2$
Solultion set= {$\displaystyle -4 \leq x \leq 2$} or [-4, 2]