Solve the Inequality for x 37>7-6x>-17

$37 > 7 - 6 x > - 17$

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

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$37 - 7 > - 6 x > - 17 - 7$

Subtract $7$ from $37$ .

$30 > - 6 x > - 17 - 7$

Subtract $7$ from $- 17$ .

$30 > - 6 x > - 24$

Divide each term in the inequality by $- 6$ .

$\frac{30}{- 6} < \frac{- 6 x}{- 6} < \frac{- 24}{- 6}$

Divide $30$ by $- 6$ .

$- 5 < \frac{- 6 x}{- 6} < \frac{- 24}{- 6}$

Cancel the common factor of $- 6$ .

Cancel the common factor.

$- 5 < \frac{- 6 x}{- 6} < \frac{- 24}{- 6}$

Divide $x$ by $1$ .

$- 5 < x < \frac{- 24}{- 6}$

Divide $- 24$ by $- 6$ .

$- 5 < x < 4$

The result can be shown in multiple forms.

Inequality Form:

$- 5 < x < 4$

Interval Notation:

$(- 5, 4)$