Solve the Inequality for x 1>=x/-5

$1 \geq \frac{x}{- 5}$

Step 1

Multiply both sides by $- 5$ .

$1 \cdot - 5 \leq \frac{x}{- 5} \cdot - 5$

Step 2

Simplify.

Simplify the left side.

Multiply $- 5$ by $1$ .

$- 5 \leq \frac{x}{- 5} \cdot - 5$

Simplify the right side.

Simplify $\frac{x}{- 5} \cdot - 5$ .

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$- 5 \leq \frac{x}{5 (- 1)} \cdot - 5$

Factor $5$ out of $- 5$ .

$- 5 \leq \frac{x}{5 \cdot - 1} \cdot (5 \cdot - 1)$

Cancel the common factor.

$- 5 \leq \frac{x}{5 \cdot - 1} \cdot (5 \cdot - 1)$

Rewrite the expression.

$- 5 \leq \frac{x}{- 1} \cdot - 1$

Combine $\frac{x}{- 1}$ and $- 1$ .

$- 5 \leq \frac{x \cdot - 1}{- 1}$

Simplify the expression.

Move the negative one from the denominator of $\frac{x \cdot - 1}{- 1}$ .

$- 5 \leq - 1 \cdot (x \cdot - 1)$

Rewrite $- 1 \cdot (x \cdot - 1)$ as $- (x \cdot - 1)$ .

$- 5 \leq - (x \cdot - 1)$

Move $- 1$ to the left of $x$ .

$- 5 \leq - (- 1 \cdot x)$

Rewrite $- 1 x$ as $- x$ .

$- 5 \leq - - x$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$- 5 \leq 1 x$

Multiply $x$ by $1$ .

$- 5 \leq x$

Step 3

Rewrite so $x$ is on the left side of the inequality.

$x \geq - 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 5$

Interval Notation:

$[- 5, \infty)$