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

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

Step 1

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

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

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

Subtract $3$ from $- 5$ .

$- 8 < 2 x \leq 7 - 3$

Subtract $3$ from $7$ .

$- 8 < 2 x \leq 4$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 8}{2} < \frac{2 x}{2} \leq \frac{4}{2}$

Step 3

Divide $- 8$ by $2$ .

$- 4 < \frac{2 x}{2} \leq \frac{4}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 4 < \frac{2 x}{2} \leq \frac{4}{2}$

Divide $x$ by $1$ .

$- 4 < x \leq \frac{4}{2}$

Step 5

Divide $4$ by $2$ .

$- 4 < x \leq 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 4 < x \leq 2$

Interval Notation:

$(- 4, 2]$

Step 7