Finite Math Examples

$- 12 < - 3 z - 3 < - 9$

Step 1

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

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Step 1.1

Add $3$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 + 3 < - 3 z < - 9 + 3$

Step 1.2

Add $- 12$ and $3$ .

$- 9 < - 3 z < - 9 + 3$

Step 1.3

Add $- 9$ and $3$ .

$- 9 < - 3 z < - 6$

Step 2

Divide each term in the inequality by $- 3$ .

$\frac{- 9}{- 3} > \frac{- 3 z}{- 3} > \frac{- 6}{- 3}$

Step 3

Divide $- 9$ by $- 3$ .

$3 > \frac{- 3 z}{- 3} > \frac{- 6}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

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Step 4.1

Cancel the common factor.

$3 > \frac{- 3 z}{- 3} > \frac{- 6}{- 3}$

Step 4.2

Divide $z$ by $1$ .

$3 > z > \frac{- 6}{- 3}$

Step 5

Divide $- 6$ by $- 3$ .

$3 > z > 2$

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.

$2 < z < 3$

Step 7

Convert the inequality to interval notation.

$(2, 3)$

Step 8