Solve for x -3<2x+1<=3

$- 3 < 2 x + 1 \leq 3$

Step 1

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.

$- 3 - 1 < 2 x \leq 3 - 1$

Subtract $1$ from $- 3$ .

$- 4 < 2 x \leq 3 - 1$

Subtract $1$ from $3$ .

$- 4 < 2 x \leq 2$

Step 2

Divide each term in the inequality by $2$ .

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

Step 3

Divide $- 4$ by $2$ .

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Divide $2$ by $2$ .

$- 2 < x \leq 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x \leq 1$

Interval Notation:

$(- 2, 1]$

Step 7