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

$- 3 < 2 x - 3 < 7$

Step 1

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

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

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

Add $- 3$ and $3$ .

$0 < 2 x < 7 + 3$

Add $7$ and $3$ .

$0 < 2 x < 10$

Step 2

Divide each term in the inequality by $2$ .

$\frac{0}{2} < \frac{2 x}{2} < \frac{10}{2}$

Step 3

Divide $0$ by $2$ .

$0 < \frac{2 x}{2} < \frac{10}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$0 < \frac{2 x}{2} < \frac{10}{2}$

Divide $x$ by $1$ .

$0 < x < \frac{10}{2}$

Step 5

Divide $10$ by $2$ .

$0 < x < 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$0 < x < 5$

Interval Notation:

$(0, 5)$

Step 7