Solve for m |2m+7|=6m+13

$| 2 m + 7 | = 6 m + 13$

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

$2 m + 7 = \pm (6 m + 13)$

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.

$2 m + 7 = 6 m + 13$

Move all terms containing $m$ to the left side of the equation.

Subtract $6 m$ from both sides of the equation.

$2 m + 7 - 6 m = 13$

Subtract $6 m$ from $2 m$ .

$- 4 m + 7 = 13$

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

Subtract $7$ from both sides of the equation.

$- 4 m = 13 - 7$

Subtract $7$ from $13$ .

$- 4 m = 6$

Divide each term in $- 4 m = 6$ by $- 4$ and simplify.

Divide each term in $- 4 m = 6$ by $- 4$ .

$\frac{- 4 m}{- 4} = \frac{6}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 m}{- 4} = \frac{6}{- 4}$

Divide $m$ by $1$ .

$m = \frac{6}{- 4}$

Simplify the right side.

Cancel the common factor of $6$ and $- 4$ .

Factor $2$ out of $6$ .

$m = \frac{2 (3)}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$m = \frac{2 \cdot 3}{2 \cdot - 2}$

Cancel the common factor.

$m = \frac{2 \cdot 3}{2 \cdot - 2}$

Rewrite the expression.

$m = \frac{3}{- 2}$

Move the negative in front of the fraction.

$m = - \frac{3}{2}$

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

$2 m + 7 = - (6 m + 13)$

Simplify $- (6 m + 13)$ .

Rewrite.

$2 m + 7 = 0 + 0 - (6 m + 13)$

Simplify by adding zeros.

$2 m + 7 = - (6 m + 13)$

Apply the distributive property.

$2 m + 7 = - (6 m) - 1 \cdot 13$

Multiply.

Multiply $6$ by $- 1$ .

$2 m + 7 = - 6 m - 1 \cdot 13$

Multiply $- 1$ by $13$ .

$2 m + 7 = - 6 m - 13$

Move all terms containing $m$ to the left side of the equation.

Add $6 m$ to both sides of the equation.

$2 m + 7 + 6 m = - 13$

Add $2 m$ and $6 m$ .

$8 m + 7 = - 13$

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

Subtract $7$ from both sides of the equation.

$8 m = - 13 - 7$

Subtract $7$ from $- 13$ .

$8 m = - 20$

Divide each term in $8 m = - 20$ by $8$ and simplify.

Divide each term in $8 m = - 20$ by $8$ .

$\frac{8 m}{8} = \frac{- 20}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 m}{8} = \frac{- 20}{8}$

Divide $m$ by $1$ .

$m = \frac{- 20}{8}$

Simplify the right side.

Cancel the common factor of $- 20$ and $8$ .

Factor $4$ out of $- 20$ .

$m = \frac{4 (- 5)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$m = \frac{4 \cdot - 5}{4 \cdot 2}$

Cancel the common factor.

$m = \frac{4 \cdot - 5}{4 \cdot 2}$

Rewrite the expression.

$m = \frac{- 5}{2}$

Move the negative in front of the fraction.

$m = - \frac{5}{2}$

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

$m = - \frac{3}{2}, - \frac{5}{2}$

Exclude the solutions that do not make $| 2 m + 7 | = 6 m + 13$ true.

$m = - \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{3}{2}$

Decimal Form:

$m = - 1.5$

Mixed Number Form:

$m = - 1 \frac{1}{2}$

Solve for m |2m+7|=6m+13

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