Solve the Inequality for m -4|-6m|<-24

$- 4 | - 6 m | < - 24$

Step 1

Write $- 4 | - 6 m | < - 24$ as a piecewise.

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

$- 6 m \geq 0$

Divide each term in $- 6 m \geq 0$ by $- 6$ and simplify.

Divide each term in $- 6 m \geq 0$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 m}{- 6} \leq \frac{0}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 m}{- 6} \leq \frac{0}{- 6}$

Divide $m$ by $1$ .

$m \leq \frac{0}{- 6}$

Simplify the right side.

Divide $0$ by $- 6$ .

$m \leq 0$

In the piece where $- 6 m$ is non-negative, remove the absolute value.

$- 4 (- 6 m) < - 24$

To find the interval for the second piece, find where the inside of the absolute value is negative.

$- 6 m < 0$

Divide each term in $- 6 m < 0$ by $- 6$ and simplify.

Divide each term in $- 6 m < 0$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 m}{- 6} > \frac{0}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 m}{- 6} > \frac{0}{- 6}$

Divide $m$ by $1$ .

$m > \frac{0}{- 6}$

Simplify the right side.

Divide $0$ by $- 6$ .

$m > 0$

In the piece where $- 6 m$ is negative, remove the absolute value and multiply by $- 1$ .

$- 4 (6 m) < - 24$

Write as a piecewise.

${\begin{cases} - 4 (- 6 m) < - 24 & m \leq 0 \\ - 4 (6 m) < - 24 & m > 0 \end{cases}$

Multiply $- 6$ by $- 4$ .

${\begin{cases} 24 m < - 24 & m \leq 0 \\ - 4 (6 m) < - 24 & m > 0 \end{cases}$

Multiply $6$ by $- 4$ .

${\begin{cases} 24 m < - 24 & m \leq 0 \\ - 24 m < - 24 & m > 0 \end{cases}$

Step 2

Divide each term in $24 m < - 24$ by $24$ and simplify.

Divide each term in $24 m < - 24$ by $24$ .

$\frac{24 m}{24} < \frac{- 24}{24}$

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{24 m}{24} < \frac{- 24}{24}$

Divide $m$ by $1$ .

$m < \frac{- 24}{24}$

Simplify the right side.

Divide $- 24$ by $24$ .

$m < - 1$

Step 3

Divide each term in $- 24 m < - 24$ by $- 24$ and simplify.

Divide each term in $- 24 m < - 24$ by $- 24$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 24 m}{- 24} > \frac{- 24}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 m}{- 24} > \frac{- 24}{- 24}$

Divide $m$ by $1$ .

$m > \frac{- 24}{- 24}$

Simplify the right side.

Divide $- 24$ by $- 24$ .

$m > 1$

Step 4

Find the union of the solutions.

$m < - 1$ or $m > 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$m < - 1 or m > 1$

Interval Notation:

$(- \infty, - 1) \cup (1, \infty)$

Step 6

Solve the Inequality for m -4|-6m|<-24

Related Questions

Support LCMGCF.com by disabling your adblocker.