Solve for x -34<7x-6<8

$- 34 < 7 x - 6 < 8$

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

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

$- 34 + 6 < 7 x < 8 + 6$

Add $- 34$ and $6$ .

$- 28 < 7 x < 8 + 6$

Add $8$ and $6$ .

$- 28 < 7 x < 14$

Divide each term in the inequality by $7$ .

$\frac{- 28}{7} < \frac{7 x}{7} < \frac{14}{7}$

Divide $- 28$ by $7$ .

$- 4 < \frac{7 x}{7} < \frac{14}{7}$

Cancel the common factor of $7$ .

Cancel the common factor.

$- 4 < \frac{7 x}{7} < \frac{14}{7}$

Divide $x$ by $1$ .

$- 4 < x < \frac{14}{7}$

Divide $14$ by $7$ .

$- 4 < x < 2$

The result can be shown in multiple forms.

Inequality Form:

$- 4 < x < 2$

Interval Notation:

$(- 4, 2)$