Solve for x -12<=-3x-9<15

$- 12 \leq - 3 x - 9 < 15$

Step 1

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

Add $9$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 + 9 \leq - 3 x < 15 + 9$

Add $- 12$ and $9$ .

$- 3 \leq - 3 x < 15 + 9$

Add $15$ and $9$ .

$- 3 \leq - 3 x < 24$

Step 2

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

$\frac{- 3}{- 3} \geq \frac{- 3 x}{- 3} > \frac{24}{- 3}$

Step 3

Divide $- 3$ by $- 3$ .

$1 \geq \frac{- 3 x}{- 3} > \frac{24}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$1 \geq \frac{- 3 x}{- 3} > \frac{24}{- 3}$

Divide $x$ by $1$ .

$1 \geq x > \frac{24}{- 3}$

Step 5

Divide $24$ by $- 3$ .

$1 \geq x > - 8$

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.

$- 8 < x \leq 1$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 8 < x \leq 1$

Interval Notation:

$(- 8, 1]$

Step 8