Solve for x -5<3x+1<=7

$- 5 < 3 x + 1 \leq 7$

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

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 1 < 3 x \leq 7 - 1$

Subtract $1$ from $- 5$ .

$- 6 < 3 x \leq 7 - 1$

Subtract $1$ from $7$ .

$- 6 < 3 x \leq 6$

Divide each term in the inequality by $3$ .

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

Divide $- 6$ by $3$ .

$- 2 < \frac{3 x}{3} \leq \frac{6}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 2 < \frac{3 x}{3} \leq \frac{6}{3}$

Divide $x$ by $1$ .

$- 2 < x \leq \frac{6}{3}$

Divide $6$ by $3$ .

$- 2 < x \leq 2$

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x \leq 2$

Interval Notation:

$(- 2, 2]$