Solve for x -10<=-3x-5<0

$- 10 \leq - 3 x - 5 < 0$

Step 1

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

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 10 + 5 \leq - 3 x < 0 + 5$

Add $- 10$ and $5$ .

$- 5 \leq - 3 x < 0 + 5$

Add $0$ and $5$ .

$- 5 \leq - 3 x < 5$

Step 2

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

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

Step 3

Dividing two negative values results in a positive value.

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

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Move the negative in front of the fraction.

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

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.

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

Step 7

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(- \frac{5}{3}, \frac{5}{3}]$

Step 8