Solve for m (|6-2m|)/-4-7=-19

$\frac{| 6 - 2 m |}{- 4} - 7 = - 19$

Move the negative in front of the fraction.

$- \frac{| 6 - 2 m |}{4} - 7 = - 19$

Move all terms not containing $| 6 - 2 m |$ to the right side of the equation.

Add $7$ to both sides of the equation.

$- \frac{| 6 - 2 m |}{4} = - 19 + 7$

Add $- 19$ and $7$ .

$- \frac{| 6 - 2 m |}{4} = - 12$

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{| 6 - 2 m |}{4}) = - 4 \cdot - 12$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{| 6 - 2 m |}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{| 6 - 2 m |}{4}$ into the numerator.

$- 4 \frac{- | 6 - 2 m |}{4} = - 4 \cdot - 12$

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- | 6 - 2 m |}{4} = - 4 \cdot - 12$

Cancel the common factor.

$4 \cdot - 1 \frac{- | 6 - 2 m |}{4} = - 4 \cdot - 12$

Rewrite the expression.

$- - | 6 - 2 m | = - 4 \cdot - 12$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 | 6 - 2 m | = - 4 \cdot - 12$

Multiply $| 6 - 2 m |$ by $1$ .

$| 6 - 2 m | = - 4 \cdot - 12$

Simplify the right side.

Multiply $- 4$ by $- 12$ .

$| 6 - 2 m | = 48$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$6 - 2 m = \pm 48$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$6 - 2 m = 48$

Move all terms not containing $m$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$- 2 m = 48 - 6$

Subtract $6$ from $48$ .

$- 2 m = 42$

Divide each term in $- 2 m = 42$ by $- 2$ and simplify.

Divide each term in $- 2 m = 42$ by $- 2$ .

$\frac{- 2 m}{- 2} = \frac{42}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 m}{- 2} = \frac{42}{- 2}$

Divide $m$ by $1$ .

$m = \frac{42}{- 2}$

Simplify the right side.

Divide $42$ by $- 2$ .

$m = - 21$

Next, use the negative value of the $\pm$ to find the second solution.

$6 - 2 m = - 48$

Move all terms not containing $m$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$- 2 m = - 48 - 6$

Subtract $6$ from $- 48$ .

$- 2 m = - 54$

Divide each term in $- 2 m = - 54$ by $- 2$ and simplify.

Divide each term in $- 2 m = - 54$ by $- 2$ .

$\frac{- 2 m}{- 2} = \frac{- 54}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 m}{- 2} = \frac{- 54}{- 2}$

Divide $m$ by $1$ .

$m = \frac{- 54}{- 2}$

Simplify the right side.

Divide $- 54$ by $- 2$ .

$m = 27$

The complete solution is the result of both the positive and negative portions of the solution.

$m = - 21, 27$

Solve for m (|6-2m|)/-4-7=-19

Related Questions

Support LCMGCF.com by disabling your adblocker.