Solve the Inequality for m -8<-1/4m

$- 8 < - \frac{1}{4} m$

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

$- \frac{1}{4} m > - 8$

Multiply each term in $- \frac{1}{4} m > - 8$ by $- 4$ to eliminate the fractions.

Multiply each term in $- \frac{1}{4} m > - 8$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{1}{4} m \cdot - 4 < - 8 \cdot - 4$

Simplify the left side.

Combine $m$ and $\frac{1}{4}$ .

$- \frac{m}{4} \cdot - 4 < - 8 \cdot - 4$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{m}{4}$ into the numerator.

$\frac{- m}{4} \cdot - 4 < - 8 \cdot - 4$

Factor $4$ out of $- 4$ .

$\frac{- m}{4} \cdot (4 (- 1)) < - 8 \cdot - 4$

Cancel the common factor.

$\frac{- m}{4} \cdot (4 \cdot - 1) < - 8 \cdot - 4$

Rewrite the expression.

$- m \cdot - 1 < - 8 \cdot - 4$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 m < - 8 \cdot - 4$

Multiply $m$ by $1$ .

$m < - 8 \cdot - 4$

Simplify the right side.

Multiply $- 8$ by $- 4$ .

$m < 32$

The result can be shown in multiple forms.

Inequality Form:

$m < 32$

Interval Notation:

$(- \infty, 32)$

Solve the Inequality for m -8<-1/4m

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