Solve for x -12<3x-6<=21

$- 12 < 3 x - 6 \leq 21$

Step 1

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

Add $6$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 + 6 < 3 x \leq 21 + 6$

Add $- 12$ and $6$ .

$- 6 < 3 x \leq 21 + 6$

Add $21$ and $6$ .

$- 6 < 3 x \leq 27$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 6}{3} < \frac{3 x}{3} \leq \frac{27}{3}$

Step 3

Divide $- 6$ by $3$ .

$- 2 < \frac{3 x}{3} \leq \frac{27}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 2 < \frac{3 x}{3} \leq \frac{27}{3}$

Divide $x$ by $1$ .

$- 2 < x \leq \frac{27}{3}$

Step 5

Divide $27$ by $3$ .

$- 2 < x \leq 9$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x \leq 9$

Interval Notation:

$(- 2, 9]$

Step 7