Answer
The solution set is $(-\infty, -6)$ .
Work Step by Step
The idea is to isolate x on one side.
Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains the same).
Multiplying/dividing with a negative number inverts the order (the inequality symbol changes).
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$ 1-\displaystyle \frac{x}{2} \gt 4\qquad $ ... $/\times 2$
$ 2-x \gt 8\qquad $ ... $/-2$
$-x \gt 6\qquad $ ... $/\times(-1)$ ... (negative: change direction)
$ x \lt -6$
The solution set is $(-\infty, -6)$ .
