Solve for x -5<3x-2<=7

$- 5 < 3 x - 2 \leq 7$

Step 1

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

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

$- 5 + 2 < 3 x \leq 7 + 2$

Add $- 5$ and $2$ .

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

Add $7$ and $2$ .

$- 3 < 3 x \leq 9$

Step 2

Divide each term in the inequality by $3$ .

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

Step 3

Divide $- 3$ by $3$ .

$- 1 < \frac{3 x}{3} \leq \frac{9}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 1 < \frac{3 x}{3} \leq \frac{9}{3}$

Divide $x$ by $1$ .

$- 1 < x \leq \frac{9}{3}$

Step 5

Divide $9$ by $3$ .

$- 1 < x \leq 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 1 < x \leq 3$

Interval Notation:

$(- 1, 3]$

Step 7