Solve for x -8<2x+16<14

$- 8 < 2 x + 16 < 14$

Step 1

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

Subtract $16$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 8 - 16 < 2 x < 14 - 16$

Subtract $16$ from $- 8$ .

$- 24 < 2 x < 14 - 16$

Subtract $16$ from $14$ .

$- 24 < 2 x < - 2$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 24}{2} < \frac{2 x}{2} < \frac{- 2}{2}$

Step 3

Divide $- 24$ by $2$ .

$- 12 < \frac{2 x}{2} < \frac{- 2}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 12 < \frac{2 x}{2} < \frac{- 2}{2}$

Divide $x$ by $1$ .

$- 12 < x < \frac{- 2}{2}$

Step 5

Divide $- 2$ by $2$ .

$- 12 < x < - 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 12 < x < - 1$

Interval Notation:

$(- 12, - 1)$

Step 7