Answer
$(-∞,-15]\cup[1,∞)$
Work Step by Step
$|\frac{7+x}{2}|\geq4$
$\frac{7+x}{2}\leq-4$ or $\frac{7+x}{2}\geq4$
$7+x\leq-8$ or $7+x\geq8$
$x\leq-15$ or $x\geq1$
$(-∞,-15]\cup[1,∞)$
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