Answer
$[-4, 2)$
Work Step by Step
The idea is to isolate $x$ in the middle.
Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbols remain).
Multiplying/dividing with a negative number inverts the order (the inequality symbols changes).
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$-6\displaystyle \leq\frac{1}{2}x-4 \lt -3 \qquad $ ... all parts $\times 2$
$-12\leq x-8 \lt -6 \qquad $ ... add $8$ to all parts
$-4 \leq x \lt 2 $
... left border included, right border excluded
The solution set is $[-4, 2)$ .
