Solve for m 8(3/4m+2)-3(1/6m-4)=3/2m

$8 (\frac{3}{4} m + 2) - 3 (\frac{1}{6} m - 4) = \frac{3}{2} m$

Step 1

Simplify $8 (\frac{3}{4} m + 2) - 3 (\frac{1}{6} m - 4)$ .

Simplify each term.

Combine $\frac{3}{4}$ and $m$ .

$8 (\frac{3 m}{4} + 2) - 3 (\frac{1}{6} m - 4) = \frac{3}{2} m$

Apply the distributive property.

$8 \frac{3 m}{4} + 8 \cdot 2 - 3 (\frac{1}{6} m - 4) = \frac{3}{2} m$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$4 (2) \frac{3 m}{4} + 8 \cdot 2 - 3 (\frac{1}{6} m - 4) = \frac{3}{2} m$

Cancel the common factor.

$4 \cdot 2 \frac{3 m}{4} + 8 \cdot 2 - 3 (\frac{1}{6} m - 4) = \frac{3}{2} m$

Rewrite the expression.

$2 (3 m) + 8 \cdot 2 - 3 (\frac{1}{6} m - 4) = \frac{3}{2} m$

Multiply $3$ by $2$ .

$6 m + 8 \cdot 2 - 3 (\frac{1}{6} m - 4) = \frac{3}{2} m$

Multiply $8$ by $2$ .

$6 m + 16 - 3 (\frac{1}{6} m - 4) = \frac{3}{2} m$

Combine $\frac{1}{6}$ and $m$ .

$6 m + 16 - 3 (\frac{m}{6} - 4) = \frac{3}{2} m$

Apply the distributive property.

$6 m + 16 - 3 \frac{m}{6} - 3 \cdot - 4 = \frac{3}{2} m$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$6 m + 16 + 3 (- 1) \frac{m}{6} - 3 \cdot - 4 = \frac{3}{2} m$

Factor $3$ out of $6$ .

$6 m + 16 + 3 \cdot - 1 \frac{m}{3 \cdot 2} - 3 \cdot - 4 = \frac{3}{2} m$

Cancel the common factor.

$6 m + 16 + 3 \cdot - 1 \frac{m}{3 \cdot 2} - 3 \cdot - 4 = \frac{3}{2} m$

Rewrite the expression.

$6 m + 16 - 1 \frac{m}{2} - 3 \cdot - 4 = \frac{3}{2} m$

Multiply $- 3$ by $- 4$ .

$6 m + 16 - 1 \frac{m}{2} + 12 = \frac{3}{2} m$

Rewrite $- 1 \frac{m}{2}$ as $- \frac{m}{2}$ .

$6 m + 16 - \frac{m}{2} + 12 = \frac{3}{2} m$

To write $6 m$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$6 m \cdot \frac{2}{2} - \frac{m}{2} + 16 + 12 = \frac{3}{2} m$

Combine $6 m$ and $\frac{2}{2}$ .

$\frac{6 m \cdot 2}{2} - \frac{m}{2} + 16 + 12 = \frac{3}{2} m$

Combine the numerators over the common denominator.

$\frac{6 m \cdot 2 - m}{2} + 16 + 12 = \frac{3}{2} m$

Find the common denominator.

Write $16$ as a fraction with denominator $1$ .

$\frac{6 m \cdot 2 - m}{2} + \frac{16}{1} + 12 = \frac{3}{2} m$

Multiply $\frac{16}{1}$ by $\frac{2}{2}$ .

$\frac{6 m \cdot 2 - m}{2} + \frac{16}{1} \cdot \frac{2}{2} + 12 = \frac{3}{2} m$

Multiply $\frac{16}{1}$ by $\frac{2}{2}$ .

$\frac{6 m \cdot 2 - m}{2} + \frac{16 \cdot 2}{2} + 12 = \frac{3}{2} m$

Write $12$ as a fraction with denominator $1$ .

$\frac{6 m \cdot 2 - m}{2} + \frac{16 \cdot 2}{2} + \frac{12}{1} = \frac{3}{2} m$

Multiply $\frac{12}{1}$ by $\frac{2}{2}$ .

$\frac{6 m \cdot 2 - m}{2} + \frac{16 \cdot 2}{2} + \frac{12}{1} \cdot \frac{2}{2} = \frac{3}{2} m$

Multiply $\frac{12}{1}$ by $\frac{2}{2}$ .

$\frac{6 m \cdot 2 - m}{2} + \frac{16 \cdot 2}{2} + \frac{12 \cdot 2}{2} = \frac{3}{2} m$

Combine the numerators over the common denominator.

$\frac{6 m \cdot 2 - m + 16 \cdot 2 + 12 \cdot 2}{2} = \frac{3}{2} m$

Simplify each term.

Multiply $2$ by $6$ .

$\frac{12 m - m + 16 \cdot 2 + 12 \cdot 2}{2} = \frac{3}{2} m$

Multiply $16$ by $2$ .

$\frac{12 m - m + 32 + 12 \cdot 2}{2} = \frac{3}{2} m$

Multiply $12$ by $2$ .

$\frac{12 m - m + 32 + 24}{2} = \frac{3}{2} m$

Simplify by adding terms.

Subtract $m$ from $12 m$ .

$\frac{11 m + 32 + 24}{2} = \frac{3}{2} m$

Add $32$ and $24$ .

$\frac{11 m + 56}{2} = \frac{3}{2} m$

Step 2

Combine $\frac{3}{2}$ and $m$ .

$\frac{11 m + 56}{2} = \frac{3 m}{2}$

Step 3

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

Subtract $\frac{3 m}{2}$ from both sides of the equation.

$\frac{11 m + 56}{2} - \frac{3 m}{2} = 0$

Combine the numerators over the common denominator.

$\frac{11 m + 56 - 3 m}{2} = 0$

Subtract $3 m$ from $11 m$ .

$\frac{8 m + 56}{2} = 0$

Cancel the common factor of $8 m + 56$ and $2$ .

Factor $2$ out of $8 m$ .

$\frac{2 (4 m) + 56}{2} = 0$

Factor $2$ out of $56$ .

$\frac{2 (4 m) + 2 \cdot 28}{2} = 0$

Factor $2$ out of $2 (4 m) + 2 (28)$ .

$\frac{2 (4 m + 28)}{2} = 0$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (4 m + 28)}{2 (1)} = 0$

Cancel the common factor.

$\frac{2 (4 m + 28)}{2 \cdot 1} = 0$

Rewrite the expression.

$\frac{4 m + 28}{1} = 0$

Divide $4 m + 28$ by $1$ .

$4 m + 28 = 0$

Step 4

Subtract $28$ from both sides of the equation.

$4 m = - 28$

Step 5

Divide each term in $4 m = - 28$ by $4$ and simplify.

Divide each term in $4 m = - 28$ by $4$ .

$\frac{4 m}{4} = \frac{- 28}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 m}{4} = \frac{- 28}{4}$

Divide $m$ by $1$ .

$m = \frac{- 28}{4}$

Simplify the right side.

Divide $- 28$ by $4$ .

$m = - 7$

Solve for m 8(3/4m+2)-3(1/6m-4)=3/2m

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