Solve for m (8m+6)/2+6=(10m+5)/7

$\frac{8 m + 6}{2} + 6 = \frac{10 m + 5}{7}$

Multiply both sides by $7$ .

$(\frac{8 m + 6}{2} + 6) \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Simplify.

Simplify the left side.

Simplify $(\frac{8 m + 6}{2} + 6) \cdot 7$ .

Cancel the common factor of $8 m + 6$ and $2$ .

Factor $2$ out of $8 m$ .

$(\frac{2 (4 m) + 6}{2} + 6) \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Factor $2$ out of $6$ .

$(\frac{2 (4 m) + 2 \cdot 3}{2} + 6) \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Factor $2$ out of $2 (4 m) + 2 (3)$ .

$(\frac{2 (4 m + 3)}{2} + 6) \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{2 (4 m + 3)}{2 (1)} + 6) \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Cancel the common factor.

$(\frac{2 (4 m + 3)}{2 \cdot 1} + 6) \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Rewrite the expression.

$(\frac{4 m + 3}{1} + 6) \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Divide $4 m + 3$ by $1$ .

$(4 m + 3 + 6) \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Add $3$ and $6$ .

$(4 m + 9) \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Apply the distributive property.

$4 m \cdot 7 + 9 \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Multiply.

Multiply $7$ by $4$ .

$28 m + 9 \cdot 7 = \frac{10 m + 5}{7} \cdot 7$

Multiply $9$ by $7$ .

$28 m + 63 = \frac{10 m + 5}{7} \cdot 7$

Simplify the right side.

Simplify $\frac{10 m + 5}{7} \cdot 7$ .

Factor $5$ out of $10 m + 5$ .

Factor $5$ out of $10 m$ .

$28 m + 63 = \frac{5 (2 m) + 5}{7} \cdot 7$

Factor $5$ out of $5$ .

$28 m + 63 = \frac{5 (2 m) + 5 (1)}{7} \cdot 7$

Factor $5$ out of $5 (2 m) + 5 (1)$ .

$28 m + 63 = \frac{5 (2 m + 1)}{7} \cdot 7$

Cancel the common factor of $7$ .

Cancel the common factor.

$28 m + 63 = \frac{5 (2 m + 1)}{7} \cdot 7$

Rewrite the expression.

$28 m + 63 = 5 (2 m + 1)$

Apply the distributive property.

$28 m + 63 = 5 (2 m) + 5 \cdot 1$

Multiply.

Multiply $2$ by $5$ .

$28 m + 63 = 10 m + 5 \cdot 1$

Multiply $5$ by $1$ .

$28 m + 63 = 10 m + 5$

Solve for $m$ .

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

Subtract $10 m$ from both sides of the equation.

$28 m + 63 - 10 m = 5$

Subtract $10 m$ from $28 m$ .

$18 m + 63 = 5$

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

Subtract $63$ from both sides of the equation.

$18 m = 5 - 63$

Subtract $63$ from $5$ .

$18 m = - 58$

Divide each term in $18 m = - 58$ by $18$ and simplify.

Divide each term in $18 m = - 58$ by $18$ .

$\frac{18 m}{18} = \frac{- 58}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 m}{18} = \frac{- 58}{18}$

Divide $m$ by $1$ .

$m = \frac{- 58}{18}$

Simplify the right side.

Cancel the common factor of $- 58$ and $18$ .

Factor $2$ out of $- 58$ .

$m = \frac{2 (- 29)}{18}$

Cancel the common factors.

Factor $2$ out of $18$ .

$m = \frac{2 \cdot - 29}{2 \cdot 9}$

Cancel the common factor.

$m = \frac{2 \cdot - 29}{2 \cdot 9}$

Rewrite the expression.

$m = \frac{- 29}{9}$

Move the negative in front of the fraction.

$m = - \frac{29}{9}$

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{29}{9}$

Decimal Form:

$m = - 3.\overline{2}$

Mixed Number Form:

$m = - 3 \frac{2}{9}$

Solve for m (8m+6)/2+6=(10m+5)/7

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