Solve for z -10<=3/2z+2<=-4

$- 10 \leq \frac{3}{2} z + 2 \leq - 4$

Step 1

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

$- 10 \leq \frac{3 z}{2} + 2 \leq - 4$

Step 2

Move all terms not containing $z$ 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.

$- 10 - 2 \leq \frac{3 z}{2} \leq - 4 - 2$

Subtract $2$ from $- 10$ .

$- 12 \leq \frac{3 z}{2} \leq - 4 - 2$

Multiply each term in the inequality by $2$ .

$- 12 \cdot 2 \leq \frac{3 z}{2} \cdot 2 \leq - 4 \cdot 2 - 2 \cdot 2$

Multiply $- 12$ by $2$ .

$- 24 \leq \frac{3 z}{2} \cdot 2 \leq - 4 \cdot 2 - 2 \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 24 \leq \frac{3 z}{2} \cdot 2 \leq - 4 \cdot 2 - 2 \cdot 2$

Rewrite the expression.

$- 24 \leq 3 z \leq - 4 \cdot 2 - 2 \cdot 2$

Simplify each term.

Multiply $- 4$ by $2$ .

$- 24 \leq 3 z \leq - 8 - 2 \cdot 2$

Multiply $- 2$ by $2$ .

$- 24 \leq 3 z \leq - 8 - 4$

Subtract $4$ from $- 8$ .

$- 24 \leq 3 z \leq - 12$

Step 3

Divide each term in the inequality by $3$ .

$\frac{- 24}{3} \leq \frac{3 z}{3} \leq \frac{- 12}{3}$

Step 4

Divide $- 24$ by $3$ .

$- 8 \leq \frac{3 z}{3} \leq \frac{- 12}{3}$

Step 5

Cancel the common factor of $3$ .

Cancel the common factor.

$- 8 \leq \frac{3 z}{3} \leq \frac{- 12}{3}$

Divide $z$ by $1$ .

$- 8 \leq z \leq \frac{- 12}{3}$

Step 6

Divide $- 12$ by $3$ .

$- 8 \leq z \leq - 4$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 8 \leq z \leq - 4$

Interval Notation:

$[- 8, - 4]$

Step 8

Solve for z -10<=3/2z+2<=-4

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