Solve for x -4<-6x+2<8

$- 4 < - 6 x + 2 < 8$

Step 1

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

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 4 - 2 < - 6 x < 8 - 2$

Subtract $2$ from $- 4$ .

$- 6 < - 6 x < 8 - 2$

Subtract $2$ from $8$ .

$- 6 < - 6 x < 6$

Step 2

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

$\frac{- 6}{- 6} > \frac{- 6 x}{- 6} > \frac{6}{- 6}$

Step 3

Divide $- 6$ by $- 6$ .

$1 > \frac{- 6 x}{- 6} > \frac{6}{- 6}$

Step 4

Cancel the common factor of $- 6$ .

Cancel the common factor.

$1 > \frac{- 6 x}{- 6} > \frac{6}{- 6}$

Divide $x$ by $1$ .

$1 > x > \frac{6}{- 6}$

Step 5

Divide $6$ by $- 6$ .

$1 > x > - 1$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 1 < x < 1$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 1 < x < 1$

Interval Notation:

$(- 1, 1)$

Step 8