Question

solve the following compound inequality.
$-2 \leq \frac{2d - 2}{4} < 3$
$\boxed{?} \leq d < \boxed{}$

Explanation:

Step1: Multiply all parts by 4

To eliminate the denominator, we multiply each part of the compound inequality by 4.
$$-2\times4\leq\frac{2d - 2}{4}\times4<3\times4$$
$$-8\leq2d - 2<12$$

Step2: Add 2 to all parts

We add 2 to each part to isolate the term with \(d\).
$$-8 + 2\leq2d - 2 + 2<12 + 2$$
$$-6\leq2d<14$$

Step3: Divide all parts by 2

We divide each part by 2 to solve for \(d\).
$$\frac{-6}{2}\leq\frac{2d}{2}<\frac{14}{2}$$
$$-3\leq d<7$$

Answer:

\(-3 \leq d < 7\) (So the first box is \(-3\) and the second box is \(7\))