Solve the Inequality for f -72<f/-6

$- 72 < \frac{f}{- 6}$

Multiply both sides by $- 6$ .

$- 72 \cdot - 6 > \frac{f}{- 6} \cdot - 6$

Simplify.

Simplify the left side.

Multiply $- 72$ by $- 6$ .

$432 > \frac{f}{- 6} \cdot - 6$

Simplify the right side.

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

Cancel the common factor of $6$ .

Factor $6$ out of $- 6$ .

$432 > \frac{f}{6 (- 1)} \cdot - 6$

Factor $6$ out of $- 6$ .

$432 > \frac{f}{6 \cdot - 1} \cdot (6 \cdot - 1)$

Cancel the common factor.

$432 > \frac{f}{6 \cdot - 1} \cdot (6 \cdot - 1)$

Rewrite the expression.

$432 > \frac{f}{- 1} \cdot - 1$

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

$432 > \frac{f \cdot - 1}{- 1}$

Simplify the expression.

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

$432 > - 1 \cdot (f \cdot - 1)$

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

$432 > - (f \cdot - 1)$

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

$432 > - (- 1 \cdot f)$

Rewrite $- 1 f$ as $- f$ .

$432 > - - f$

Multiply $- - f$ .

Multiply $- 1$ by $- 1$ .

$432 > 1 f$

Multiply $f$ by $1$ .

$432 > f$

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

$f < 432$

The result can be shown in multiple forms.

Inequality Form:

$f < 432$

Interval Notation:

$(- \infty, 432)$