Solve for x -2<3x+4<=13

$- 2 < 3 x + 4 \leq 13$

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

Subtract $4$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 2 - 4 < 3 x \leq 13 - 4$

Subtract $4$ from $- 2$ .

$- 6 < 3 x \leq 13 - 4$

Subtract $4$ from $13$ .

$- 6 < 3 x \leq 9$

Divide each term in the inequality by $3$ .

$\frac{- 6}{3} < \frac{3 x}{3} \leq \frac{9}{3}$

Divide $- 6$ by $3$ .

$- 2 < \frac{3 x}{3} \leq \frac{9}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 2 < \frac{3 x}{3} \leq \frac{9}{3}$

Divide $x$ by $1$ .

$- 2 < x \leq \frac{9}{3}$

Divide $9$ by $3$ .

$- 2 < x \leq 3$

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x \leq 3$

Interval Notation:

$(- 2, 3]$