Solve the Inequality for x 0<2x-5<9

$0 < 2 x - 5 < 9$

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.

$0 + 5 < 2 x < 9 + 5$

Add $0$ and $5$ .

$5 < 2 x < 9 + 5$

Add $9$ and $5$ .

$5 < 2 x < 14$

Step 2

Divide each term in the inequality by $2$ .

$\frac{5}{2} < \frac{2 x}{2} < \frac{14}{2}$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5}{2} < \frac{2 x}{2} < \frac{14}{2}$

Divide $x$ by $1$ .

$\frac{5}{2} < x < \frac{14}{2}$

Step 4

Divide $14$ by $2$ .

$\frac{5}{2} < x < 7$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$\frac{5}{2} < x < 7$

Interval Notation:

$(\frac{5}{2}, 7)$

Step 6