Solve for x -3<2x+7<=13

$- 3 < 2 x + 7 \leq 13$

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

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 3 - 7 < 2 x \leq 13 - 7$

Subtract $7$ from $- 3$ .

$- 10 < 2 x \leq 13 - 7$

Subtract $7$ from $13$ .

$- 10 < 2 x \leq 6$

Divide each term in the inequality by $2$ .

$\frac{- 10}{2} < \frac{2 x}{2} \leq \frac{6}{2}$

Divide $- 10$ by $2$ .

$- 5 < \frac{2 x}{2} \leq \frac{6}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 < \frac{2 x}{2} \leq \frac{6}{2}$

Divide $x$ by $1$ .

$- 5 < x \leq \frac{6}{2}$

Divide $6$ by $2$ .

$- 5 < x \leq 3$

The result can be shown in multiple forms.

Inequality Form:

$- 5 < x \leq 3$

Interval Notation:

$(- 5, 3]$