Solve for x -8<=3/2x-2<=-5

$- 8 \leq \frac{3}{2} x - 2 \leq - 5$

Combine $\frac{3}{2}$ and $x$ .

$- 8 \leq \frac{3 x}{2} - 2 \leq - 5$

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

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

$- 8 + 2 \leq \frac{3 x}{2} \leq - 5 + 2$

Add $- 8$ and $2$ .

$- 6 \leq \frac{3 x}{2} \leq - 5 + 2$

Multiply each term in the inequality by $2$ .

$- 6 \cdot 2 \leq \frac{3 x}{2} \cdot 2 \leq - 5 \cdot 2 + 2 \cdot 2$

Multiply $- 6$ by $2$ .

$- 12 \leq \frac{3 x}{2} \cdot 2 \leq - 5 \cdot 2 + 2 \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 12 \leq \frac{3 x}{2} \cdot 2 \leq - 5 \cdot 2 + 2 \cdot 2$

Rewrite the expression.

$- 12 \leq 3 x \leq - 5 \cdot 2 + 2 \cdot 2$

Simplify each term.

Multiply $- 5$ by $2$ .

$- 12 \leq 3 x \leq - 10 + 2 \cdot 2$

Multiply $2$ by $2$ .

$- 12 \leq 3 x \leq - 10 + 4$

Add $- 10$ and $4$ .

$- 12 \leq 3 x \leq - 6$

Divide each term in the inequality by $3$ .

$\frac{- 12}{3} \leq \frac{3 x}{3} \leq \frac{- 6}{3}$

Divide $- 12$ by $3$ .

$- 4 \leq \frac{3 x}{3} \leq \frac{- 6}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 4 \leq \frac{3 x}{3} \leq \frac{- 6}{3}$

Divide $x$ by $1$ .

$- 4 \leq x \leq \frac{- 6}{3}$

Divide $- 6$ by $3$ .

$- 4 \leq x \leq - 2$

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x \leq - 2$

Interval Notation:

$[- 4, - 2]$