Solve the Inequality for x x/-6>=-20

$\frac{x}{- 6} \geq - 20$

Step 1

Multiply both sides by $- 6$ .

$\frac{x}{- 6} \cdot - 6 \leq - 20 \cdot - 6$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{x}{- 6} \cdot - 6$ .

Cancel the common factor of $6$ .

Factor $6$ out of $- 6$ .

$\frac{x}{6 (- 1)} \cdot - 6 \leq - 20 \cdot - 6$

Factor $6$ out of $- 6$ .

$\frac{x}{6 \cdot - 1} \cdot (6 \cdot - 1) \leq - 20 \cdot - 6$

Cancel the common factor.

$\frac{x}{6 \cdot - 1} \cdot (6 \cdot - 1) \leq - 20 \cdot - 6$

Rewrite the expression.

$\frac{x}{- 1} \cdot - 1 \leq - 20 \cdot - 6$

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

$\frac{x \cdot - 1}{- 1} \leq - 20 \cdot - 6$

Simplify the expression.

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

$- 1 \cdot (x \cdot - 1) \leq - 20 \cdot - 6$

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

$- (x \cdot - 1) \leq - 20 \cdot - 6$

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

$- (- 1 \cdot x) \leq - 20 \cdot - 6$

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

$- - x \leq - 20 \cdot - 6$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$1 x \leq - 20 \cdot - 6$

Multiply $x$ by $1$ .

$x \leq - 20 \cdot - 6$

Simplify the right side.

Multiply $- 20$ by $- 6$ .

$x \leq 120$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \leq 120$

Interval Notation:

$(- \infty, 120]$