Question

solve for r.
-10 < \frac{-3r - 11}{2} \leq 2
write your answer as a compound inequality with integers.

Explanation:

Step1: Multiply all parts by 2

$$-10 \times 2 < \frac{-3r - 11}{2} \times 2 \leq 2 \times 2$$
$$-20 < -3r - 11 \leq 4$$

Step2: Add 11 to all parts

$$-20 + 11 < -3r - 11 + 11 \leq 4 + 11$$
$$-9 < -3r \leq 15$$

Step3: Divide by -3, reverse inequalities

$$\frac{-9}{-3} > \frac{-3r}{-3} \geq \frac{15}{-3}$$
$$3 > r \geq -5$$

Step4: Rewrite in standard order

$$-5 \leq r < 3$$

Answer:

$\boldsymbol{-5 \leq r < 3}$