Solve the Inequality for d -1<=(d+2)/5<=6/5

$- 1 \leq \frac{d + 2}{5} \leq \frac{6}{5}$

Multiply each term in the inequality by $5$ .

$- 1 \cdot 5 \leq \frac{d + 2}{5} \cdot 5 \leq \frac{6}{5} \cdot 5$

Multiply $- 1$ by $5$ .

$- 5 \leq \frac{d + 2}{5} \cdot 5 \leq \frac{6}{5} \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$- 5 \leq \frac{d + 2}{5} \cdot 5 \leq \frac{6}{5} \cdot 5$

Rewrite the expression.

$- 5 \leq d + 2 \leq \frac{6}{5} \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$- 5 \leq d + 2 \leq \frac{6}{5} \cdot 5$

Rewrite the expression.

$- 5 \leq d + 2 \leq 6$

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

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 2 \leq d \leq 6 - 2$

Subtract $2$ from $- 5$ .

$- 7 \leq d \leq 6 - 2$

Subtract $2$ from $6$ .

$- 7 \leq d \leq 4$

The result can be shown in multiple forms.

Inequality Form:

$- 7 \leq d \leq 4$

Interval Notation:

$[- 7, 4]$