Solve the Inequality for x -50<7x+6<-8

$- 50 < 7 x + 6 < - 8$

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

Subtract $6$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 50 - 6 < 7 x < - 8 - 6$

Subtract $6$ from $- 50$ .

$- 56 < 7 x < - 8 - 6$

Subtract $6$ from $- 8$ .

$- 56 < 7 x < - 14$

Divide each term in the inequality by $7$ .

$\frac{- 56}{7} < \frac{7 x}{7} < \frac{- 14}{7}$

Divide $- 56$ by $7$ .

$- 8 < \frac{7 x}{7} < \frac{- 14}{7}$

Cancel the common factor of $7$ .

Cancel the common factor.

$- 8 < \frac{7 x}{7} < \frac{- 14}{7}$

Divide $x$ by $1$ .

$- 8 < x < \frac{- 14}{7}$

Divide $- 14$ by $7$ .

$- 8 < x < - 2$

The result can be shown in multiple forms.

Inequality Form:

$- 8 < x < - 2$

Interval Notation:

$(- 8, - 2)$