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

$- 3 < 2 x - 5 < 7$

Step 1

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

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

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

Add $- 3$ and $5$ .

$2 < 2 x < 7 + 5$

Add $7$ and $5$ .

$2 < 2 x < 12$

Step 2

Divide each term in the inequality by $2$ .

$\frac{2}{2} < \frac{2 x}{2} < \frac{12}{2}$

Step 3

Divide $2$ by $2$ .

$1 < \frac{2 x}{2} < \frac{12}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$1 < \frac{2 x}{2} < \frac{12}{2}$

Divide $x$ by $1$ .

$1 < x < \frac{12}{2}$

Step 5

Divide $12$ by $2$ .

$1 < x < 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$1 < x < 6$

Interval Notation:

$(1, 6)$

Step 7