Solve the Inequality for x -5<5+2x<11

$- 5 < 5 + 2 x < 11$

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.

$- 5 - 5 < 2 x < 11 - 5$

Subtract $5$ from $- 5$ .

$- 10 < 2 x < 11 - 5$

Subtract $5$ from $11$ .

$- 10 < 2 x < 6$

Divide each term in the inequality by $2$ .

$\frac{- 10}{2} < \frac{2 x}{2} < \frac{6}{2}$

Divide $- 10$ by $2$ .

$- 5 < \frac{2 x}{2} < \frac{6}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 < \frac{2 x}{2} < \frac{6}{2}$

Divide $x$ by $1$ .

$- 5 < x < \frac{6}{2}$

Divide $6$ by $2$ .

$- 5 < x < 3$

The result can be shown in multiple forms.

Inequality Form:

$- 5 < x < 3$

Interval Notation:

$(- 5, 3)$