Question

solve for d.
\\(\frac{-13d - 7}{2} \leq 3\\) or \\(-3d - 4 \geq 11\\)
write your answer as a compound inequality with integers.

Explanation:

Step1: Solve first inequality, multiply by 2

$$\frac{-13d - 7}{2} \times 2 \leq 3 \times 2$$
$$-13d - 7 \leq 6$$

Step2: Isolate term with d

$$-13d \leq 6 + 7$$
$$-13d \leq 13$$

Step3: Divide by -13, flip inequality

$$d \geq \frac{13}{-13}$$
$$d \geq -1$$

Step4: Solve second inequality, isolate term with d

$$-3d - 4 \geq 11$$
$$-3d \geq 11 + 4$$
$$-3d \geq 15$$

Step5: Divide by -3, flip inequality

$$d \leq \frac{15}{-3}$$
$$d \leq -5$$

Answer:

$d \leq -5$ or $d \geq -1$