Solve for x -6<=3x+15<9

$- 6 \leq 3 x + 15 < 9$

Step 1

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

Subtract $15$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 - 15 \leq 3 x < 9 - 15$

Subtract $15$ from $- 6$ .

$- 21 \leq 3 x < 9 - 15$

Subtract $15$ from $9$ .

$- 21 \leq 3 x < - 6$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 21}{3} \leq \frac{3 x}{3} < \frac{- 6}{3}$

Step 3

Divide $- 21$ by $3$ .

$- 7 \leq \frac{3 x}{3} < \frac{- 6}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 7 \leq \frac{3 x}{3} < \frac{- 6}{3}$

Divide $x$ by $1$ .

$- 7 \leq x < \frac{- 6}{3}$

Step 5

Divide $- 6$ by $3$ .

$- 7 \leq x < - 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 7 \leq x < - 2$

Interval Notation:

$[- 7, - 2)$

Step 7