Solve for z -9<=5/2z+1<=-4

$- 9 \leq \frac{5}{2} z + 1 \leq - 4$

Step 1

Combine $\frac{5}{2}$ and $z$ .

$- 9 \leq \frac{5 z}{2} + 1 \leq - 4$

Step 2

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

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

$- 9 - 1 \leq \frac{5 z}{2} \leq - 4 - 1$

Subtract $1$ from $- 9$ .

$- 10 \leq \frac{5 z}{2} \leq - 4 - 1$

Multiply each term in the inequality by $2$ .

$- 10 \cdot 2 \leq \frac{5 z}{2} \cdot 2 \leq - 4 \cdot 2 - 1 \cdot 2$

Multiply $- 10$ by $2$ .

$- 20 \leq \frac{5 z}{2} \cdot 2 \leq - 4 \cdot 2 - 1 \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 20 \leq \frac{5 z}{2} \cdot 2 \leq - 4 \cdot 2 - 1 \cdot 2$

Rewrite the expression.

$- 20 \leq 5 z \leq - 4 \cdot 2 - 1 \cdot 2$

Simplify each term.

Multiply $- 4$ by $2$ .

$- 20 \leq 5 z \leq - 8 - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$- 20 \leq 5 z \leq - 8 - 2$

Subtract $2$ from $- 8$ .

$- 20 \leq 5 z \leq - 10$

Step 3

Divide each term in the inequality by $5$ .

$\frac{- 20}{5} \leq \frac{5 z}{5} \leq \frac{- 10}{5}$

Step 4

Divide $- 20$ by $5$ .

$- 4 \leq \frac{5 z}{5} \leq \frac{- 10}{5}$

Step 5

Cancel the common factor of $5$ .

Cancel the common factor.

$- 4 \leq \frac{5 z}{5} \leq \frac{- 10}{5}$

Divide $z$ by $1$ .

$- 4 \leq z \leq \frac{- 10}{5}$

Step 6

Divide $- 10$ by $5$ .

$- 4 \leq z \leq - 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq z \leq - 2$

Interval Notation:

$[- 4, - 2]$

Step 8

Solve for z -9<=5/2z+1<=-4

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