Solve for x -8<1-6x<5

$- 8 < 1 - 6 x < 5$

Step 1

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

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 8 - 1 < - 6 x < 5 - 1$

Subtract $1$ from $- 8$ .

$- 9 < - 6 x < 5 - 1$

Subtract $1$ from $5$ .

$- 9 < - 6 x < 4$

Step 2

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

$\frac{- 9}{- 6} > \frac{- 6 x}{- 6} > \frac{4}{- 6}$

Step 3

Cancel the common factor of $- 9$ and $- 6$ .

Factor $- 3$ out of $- 9$ .

$\frac{- 3 \cdot 3}{- 6} > \frac{- 6 x}{- 6} > \frac{4}{- 6}$

Cancel the common factors.

Factor $- 3$ out of $- 6$ .

$\frac{- 3 \cdot 3}{- 3 \cdot 2} > \frac{- 6 x}{- 6} > \frac{4}{- 6}$

Cancel the common factor.

$\frac{- 3 \cdot 3}{- 3 \cdot 2} > \frac{- 6 x}{- 6} > \frac{4}{- 6}$

Rewrite the expression.

$\frac{3}{2} > \frac{- 6 x}{- 6} > \frac{4}{- 6}$

Step 4

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{3}{2} > \frac{- 6 x}{- 6} > \frac{4}{- 6}$

Divide $x$ by $1$ .

$\frac{3}{2} > x > \frac{4}{- 6}$

Step 5

Cancel the common factor of $4$ and $- 6$ .

Factor $2$ out of $4$ .

$\frac{3}{2} > x > \frac{2 (2)}{- 6}$

Cancel the common factors.

Factor $2$ out of $- 6$ .

$\frac{3}{2} > x > \frac{2 \cdot 2}{2 \cdot - 3}$

Cancel the common factor.

$\frac{3}{2} > x > \frac{2 \cdot 2}{2 \cdot - 3}$

Rewrite the expression.

$\frac{3}{2} > x > \frac{2}{- 3}$

Step 6

Move the negative in front of the fraction.

$\frac{3}{2} > x > - \frac{2}{3}$

Step 7

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

$- \frac{2}{3} < x < \frac{3}{2}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$- \frac{2}{3} < x < \frac{3}{2}$

Interval Notation:

$(- \frac{2}{3}, \frac{3}{2})$

Step 9

Solve for x -8<1-6x<5

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