Solve the Inequality for x -30<x/-4

$- 30 < \frac{x}{- 4}$

Step 1

Multiply both sides by $- 4$ .

$- 30 \cdot - 4 > \frac{x}{- 4} \cdot - 4$

Step 2

Simplify.

Simplify the left side.

Multiply $- 30$ by $- 4$ .

$120 > \frac{x}{- 4} \cdot - 4$

Simplify the right side.

Simplify $\frac{x}{- 4} \cdot - 4$ .

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$120 > \frac{x}{4 (- 1)} \cdot - 4$

Factor $4$ out of $- 4$ .

$120 > \frac{x}{4 \cdot - 1} \cdot (4 \cdot - 1)$

Cancel the common factor.

$120 > \frac{x}{4 \cdot - 1} \cdot (4 \cdot - 1)$

Rewrite the expression.

$120 > \frac{x}{- 1} \cdot - 1$

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

$120 > \frac{x \cdot - 1}{- 1}$

Simplify the expression.

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

$120 > - 1 \cdot (x \cdot - 1)$

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

$120 > - (x \cdot - 1)$

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

$120 > - (- 1 \cdot x)$

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

$120 > - - x$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$120 > 1 x$

Multiply $x$ by $1$ .

$120 > x$

Step 3

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

$x < 120$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 120$

Interval Notation:

$(- \infty, 120)$