Solve the Inequality for x 6<1-3x<=10

$6 < 1 - 3 x \leq 10$

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.

$6 - 1 < - 3 x \leq 10 - 1$

Subtract $1$ from $6$ .

$5 < - 3 x \leq 10 - 1$

Subtract $1$ from $10$ .

$5 < - 3 x \leq 9$

Divide each term in the inequality by $- 3$ .

$\frac{5}{- 3} > \frac{- 3 x}{- 3} \geq \frac{9}{- 3}$

Move the negative in front of the fraction.

$- \frac{5}{3} > \frac{- 3 x}{- 3} \geq \frac{9}{- 3}$

Cancel the common factor of $- 3$ .

Cancel the common factor.

$- \frac{5}{3} > \frac{- 3 x}{- 3} \geq \frac{9}{- 3}$

Divide $x$ by $1$ .

$- \frac{5}{3} > x \geq \frac{9}{- 3}$

Divide $9$ by $- 3$ .

$- \frac{5}{3} > x \geq - 3$

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

$- 3 \leq x < - \frac{5}{3}$

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq x < - \frac{5}{3}$

Interval Notation:

$[- 3, - \frac{5}{3})$