Solve for d -2<=(2d-2)/4<3

$- 2 \leq \frac{2 d - 2}{4} < 3$

Cancel the common factor of $2 d - 2$ and $4$ .

Factor $2$ out of $2 d$ .

$- 2 \leq \frac{2 (d) - 2}{4} < 3$

Factor $2$ out of $- 2$ .

$- 2 \leq \frac{2 (d) + 2 (- 1)}{4} < 3$

Factor $2$ out of $2 (d) + 2 (- 1)$ .

$- 2 \leq \frac{2 (d - 1)}{4} < 3$

Cancel the common factors.

Factor $2$ out of $4$ .

$- 2 \leq \frac{2 (d - 1)}{2 (2)} < 3$

Cancel the common factor.

$- 2 \leq \frac{2 (d - 1)}{2 \cdot 2} < 3$

Rewrite the expression.

$- 2 \leq \frac{d - 1}{2} < 3$

Multiply each term in the inequality by $2$ .

$- 2 \cdot 2 \leq \frac{d - 1}{2} \cdot 2 < 3 \cdot 2$

Multiply $- 2$ by $2$ .

$- 4 \leq \frac{d - 1}{2} \cdot 2 < 3 \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 4 \leq \frac{d - 1}{2} \cdot 2 < 3 \cdot 2$

Rewrite the expression.

$- 4 \leq d - 1 < 3 \cdot 2$

Multiply $3$ by $2$ .

$- 4 \leq d - 1 < 6$

Move all terms not containing $d$ from the center section of the inequality.

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 4 + 1 \leq d < 6 + 1$

Add $- 4$ and $1$ .

$- 3 \leq d < 6 + 1$

Add $6$ and $1$ .

$- 3 \leq d < 7$

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq d < 7$

Interval Notation:

$[- 3, 7)$