Solve for x -1<-3x<=1

$- 1 < - 3 x \leq 1$

Step 1

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

$\frac{- 1}{- 3} > \frac{- 3 x}{- 3} \geq \frac{1}{- 3}$

Step 2

Dividing two negative values results in a positive value.

$\frac{1}{3} > \frac{- 3 x}{- 3} \geq \frac{1}{- 3}$

Step 3

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{1}{3} > \frac{- 3 x}{- 3} \geq \frac{1}{- 3}$

Divide $x$ by $1$ .

$\frac{1}{3} > x \geq \frac{1}{- 3}$

Step 4

Move the negative in front of the fraction.

$\frac{1}{3} > x \geq - \frac{1}{3}$

Step 5

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

$- \frac{1}{3} \leq x < \frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- \frac{1}{3} \leq x < \frac{1}{3}$

Interval Notation:

$[- \frac{1}{3}, \frac{1}{3})$

Step 7