Solve for x -4<3x+2<=8

$- 4 < 3 x + 2 \leq 8$

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

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 4 - 2 < 3 x \leq 8 - 2$

Subtract $2$ from $- 4$ .

$- 6 < 3 x \leq 8 - 2$

Subtract $2$ from $8$ .

$- 6 < 3 x \leq 6$

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:

$(- 2, 2]$