In Exercises 51–58, solve each compound inequality. - 3 ≤ (2/3)x - 5 < - 1

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Start by writing the compound inequality clearly: $-3 \leq \frac{2}{3}x - 5 < -1$.

Add 5 to all three parts of the inequality to isolate the term with $x$: $-3 + 5 \leq \frac{2}{3}x - 5 + 5 < -1 + 5$.

Simplify each part: $2 \leq \frac{2}{3}x < 4$.

Multiply all parts of the inequality by the reciprocal of $\frac{2}{3}$, which is $\frac{3}{2}$, to solve for $x$: $2 \times \frac{3}{2} \leq x < 4 \times \frac{3}{2}$.

Simplify the multiplication to find the range of $x$: $3 \leq x < 6$.

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