Solve for x -4<3x+5<=11

$- 4 < 3 x + 5 \leq 11$

Step 1

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

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 4 - 5 < 3 x \leq 11 - 5$

Subtract $5$ from $- 4$ .

$- 9 < 3 x \leq 11 - 5$

Subtract $5$ from $11$ .

$- 9 < 3 x \leq 6$

Step 2

Divide each term in the inequality by $3$ .

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

Step 3

Divide $- 9$ by $3$ .

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Divide $6$ by $3$ .

$- 3 < x \leq 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x \leq 2$

Interval Notation:

$(- 3, 2]$

Step 7