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

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

Step 1

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

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

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

Subtract $9$ from $- 9$ .

$- 18 < 3 x \leq 3 - 9$

Subtract $9$ from $3$ .

$- 18 < 3 x \leq - 6$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 18}{3} < \frac{3 x}{3} \leq \frac{- 6}{3}$

Step 3

Divide $- 18$ by $3$ .

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Divide $- 6$ by $3$ .

$- 6 < x \leq - 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 6 < x \leq - 2$

Interval Notation:

$(- 6, - 2]$

Step 7