Solve the Inequality for w w/-5>=9

$\frac{w}{- 5} \geq 9$

Step 1

Multiply both sides by $- 5$ .

$\frac{w}{- 5} \cdot - 5 \leq 9 \cdot - 5$

Step 2

Simplify.

Simplify the left side.

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

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$\frac{w}{5 (- 1)} \cdot - 5 \leq 9 \cdot - 5$

Factor $5$ out of $- 5$ .

$\frac{w}{5 \cdot - 1} \cdot (5 \cdot - 1) \leq 9 \cdot - 5$

Cancel the common factor.

$\frac{w}{5 \cdot - 1} \cdot (5 \cdot - 1) \leq 9 \cdot - 5$

Rewrite the expression.

$\frac{w}{- 1} \cdot - 1 \leq 9 \cdot - 5$

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

$\frac{w \cdot - 1}{- 1} \leq 9 \cdot - 5$

Simplify the expression.

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

$- 1 \cdot (w \cdot - 1) \leq 9 \cdot - 5$

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

$- (w \cdot - 1) \leq 9 \cdot - 5$

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

$- (- 1 \cdot w) \leq 9 \cdot - 5$

Rewrite $- 1 w$ as $- w$ .

$- - w \leq 9 \cdot - 5$

Multiply $- - w$ .

Multiply $- 1$ by $- 1$ .

$1 w \leq 9 \cdot - 5$

Multiply $w$ by $1$ .

$w \leq 9 \cdot - 5$

Simplify the right side.

Multiply $9$ by $- 5$ .

$w \leq - 45$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$w \leq - 45$

Interval Notation:

$(- \infty, - 45]$