Solve for x -8<2x-5<5

$- 8 < 2 x - 5 < 5$

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.

$- 8 + 5 < 2 x < 5 + 5$

Add $- 8$ and $5$ .

$- 3 < 2 x < 5 + 5$

Add $5$ and $5$ .

$- 3 < 2 x < 10$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 3}{2} < \frac{2 x}{2} < \frac{10}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{3}{2} < \frac{2 x}{2} < \frac{10}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{3}{2} < \frac{2 x}{2} < \frac{10}{2}$

Divide $x$ by $1$ .

$- \frac{3}{2} < x < \frac{10}{2}$

Step 5

Divide $10$ by $2$ .

$- \frac{3}{2} < x < 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- \frac{3}{2} < x < 5$

Interval Notation:

$(- \frac{3}{2}, 5)$

Step 7