Solve the Inequality for x -8<2x+5<7

$- 8 < 2 x + 5 < 7$

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

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

$- 8 - 5 < 2 x < 7 - 5$

Subtract $5$ from $- 8$ .

$- 13 < 2 x < 7 - 5$

Subtract $5$ from $7$ .

$- 13 < 2 x < 2$

Divide each term in the inequality by $2$ .

$\frac{- 13}{2} < \frac{2 x}{2} < \frac{2}{2}$

Move the negative in front of the fraction.

$- \frac{13}{2} < \frac{2 x}{2} < \frac{2}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{13}{2} < \frac{2 x}{2} < \frac{2}{2}$

Divide $x$ by $1$ .

$- \frac{13}{2} < x < \frac{2}{2}$

Divide $2$ by $2$ .

$- \frac{13}{2} < x < 1$

The result can be shown in multiple forms.

Inequality Form:

$- \frac{13}{2} < x < 1$

Interval Notation:

$(- \frac{13}{2}, 1)$