Solve for x -3<2x-1<=5

$- 3 < 2 x - 1 \leq 5$

Step 1

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

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 3 + 1 < 2 x \leq 5 + 1$

Add $- 3$ and $1$ .

$- 2 < 2 x \leq 5 + 1$

Add $5$ and $1$ .

$- 2 < 2 x \leq 6$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 2}{2} < \frac{2 x}{2} \leq \frac{6}{2}$

Step 3

Divide $- 2$ by $2$ .

$- 1 < \frac{2 x}{2} \leq \frac{6}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 1 < \frac{2 x}{2} \leq \frac{6}{2}$

Divide $x$ by $1$ .

$- 1 < x \leq \frac{6}{2}$

Step 5

Divide $6$ by $2$ .

$- 1 < x \leq 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 1 < x \leq 3$

Interval Notation:

$(- 1, 3]$

Step 7