Solve for x 3<2x-1<5

$3 < 2 x - 1 < 5$

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.

$3 + 1 < 2 x < 5 + 1$

Add $3$ and $1$ .

$4 < 2 x < 5 + 1$

Add $5$ and $1$ .

$4 < 2 x < 6$

Step 2

Divide each term in the inequality by $2$ .

$\frac{4}{2} < \frac{2 x}{2} < \frac{6}{2}$

Step 3

Divide $4$ by $2$ .

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Divide $6$ by $2$ .

$2 < x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$2 < x < 3$

Interval Notation:

$(2, 3)$

Step 7