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

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

Step 1

Multiply each term in the inequality by $3$ .

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

Step 2

Multiply $- 4$ by $3$ .

$- 12 \leq \frac{d + 2}{3} \cdot 3 < 2 \cdot 3$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$- 12 \leq \frac{d + 2}{3} \cdot 3 < 2 \cdot 3$

Rewrite the expression.

$- 12 \leq d + 2 < 2 \cdot 3$

Step 4

Multiply $2$ by $3$ .

$- 12 \leq d + 2 < 6$

Step 5

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.

$- 12 - 2 \leq d < 6 - 2$

Subtract $2$ from $- 12$ .

$- 14 \leq d < 6 - 2$

Subtract $2$ from $6$ .

$- 14 \leq d < 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 14 \leq d < 4$

Interval Notation:

$[- 14, 4)$

Step 7