Answer
$[3, 6)$
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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$-3\displaystyle \leq\frac{2}{3}x-5 \lt -1 \qquad $ ... all parts $\times 3$
$-9\leq 2x-15 \lt -3 \qquad $ ... add $15$ to all parts
$ 6 \leq 2x \lt 12 \qquad $ ... divide all by 2
$3 \leq x \lt 6 $
... left border included, right border excluded
The solution set is $[3, 6)$ .
