Pre-Algebra Examples

$7 < - 2 z - 1 < 9$

Step 1

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

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Step 1.1

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

$7 + 1 < - 2 z < 9 + 1$

Step 1.2

Add $7$ and $1$ .

$8 < - 2 z < 9 + 1$

Step 1.3

Add $9$ and $1$ .

$8 < - 2 z < 10$

Step 2

Divide each term in the inequality by $- 2$ .

$\frac{8}{- 2} > \frac{- 2 z}{- 2} > \frac{10}{- 2}$

Step 3

Divide $8$ by $- 2$ .

$- 4 > \frac{- 2 z}{- 2} > \frac{10}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

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Step 4.1

Cancel the common factor.

$- 4 > \frac{- 2 z}{- 2} > \frac{10}{- 2}$

Step 4.2

Divide $z$ by $1$ .

$- 4 > z > \frac{10}{- 2}$

Step 5

Divide $10$ by $- 2$ .

$- 4 > z > - 5$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 5 < z < - 4$

Step 7