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

$- 5 \leq - 10 x < 5$

Divide each term in the inequality by $- 10$ .

$\frac{- 5}{- 10} \geq \frac{- 10 x}{- 10} > \frac{5}{- 10}$

Cancel the common factor of $- 5$ and $- 10$ .

Factor $- 5$ out of $- 5$ .

$\frac{- 5 \cdot 1}{- 10} \geq \frac{- 10 x}{- 10} > \frac{5}{- 10}$

Cancel the common factors.

Factor $- 5$ out of $- 10$ .

$\frac{- 5 \cdot 1}{- 5 \cdot 2} \geq \frac{- 10 x}{- 10} > \frac{5}{- 10}$

Cancel the common factor.

$\frac{- 5 \cdot 1}{- 5 \cdot 2} \geq \frac{- 10 x}{- 10} > \frac{5}{- 10}$

Rewrite the expression.

$\frac{1}{2} \geq \frac{- 10 x}{- 10} > \frac{5}{- 10}$

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{1}{2} \geq \frac{- 10 x}{- 10} > \frac{5}{- 10}$

Divide $x$ by $1$ .

$\frac{1}{2} \geq x > \frac{5}{- 10}$

Cancel the common factor of $5$ and $- 10$ .

Factor $5$ out of $5$ .

$\frac{1}{2} \geq x > \frac{5 (1)}{- 10}$

Cancel the common factors.

Factor $5$ out of $- 10$ .

$\frac{1}{2} \geq x > \frac{5 \cdot 1}{5 \cdot - 2}$

Cancel the common factor.

$\frac{1}{2} \geq x > \frac{5 \cdot 1}{5 \cdot - 2}$

Rewrite the expression.

$\frac{1}{2} \geq x > \frac{1}{- 2}$

Move the negative in front of the fraction.

$\frac{1}{2} \geq x > - \frac{1}{2}$

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

$- \frac{1}{2} < x \leq \frac{1}{2}$

The result can be shown in multiple forms.

Inequality Form:

$- \frac{1}{2} < x \leq \frac{1}{2}$

Interval Notation:

$(- \frac{1}{2}, \frac{1}{2}]$