Solve for m 9(m+5)-3(m-2)=8m+31

$9 (m + 5) - 3 (m - 2) = 8 m + 31$

Step 1

Simplify $9 (m + 5) - 3 (m - 2)$ .

Simplify each term.

Apply the distributive property.

$9 m + 9 \cdot 5 - 3 (m - 2) = 8 m + 31$

Multiply $9$ by $5$ .

$9 m + 45 - 3 (m - 2) = 8 m + 31$

Apply the distributive property.

$9 m + 45 - 3 m - 3 \cdot - 2 = 8 m + 31$

Multiply $- 3$ by $- 2$ .

$9 m + 45 - 3 m + 6 = 8 m + 31$

Simplify by adding terms.

Subtract $3 m$ from $9 m$ .

$6 m + 45 + 6 = 8 m + 31$

Add $45$ and $6$ .

$6 m + 51 = 8 m + 31$

Step 2

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

Subtract $8 m$ from both sides of the equation.

$6 m + 51 - 8 m = 31$

Subtract $8 m$ from $6 m$ .

$- 2 m + 51 = 31$

Step 3

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

Subtract $51$ from both sides of the equation.

$- 2 m = 31 - 51$

Subtract $51$ from $31$ .

$- 2 m = - 20$

Step 4

Divide each term in $- 2 m = - 20$ by $- 2$ and simplify.

Divide each term in $- 2 m = - 20$ by $- 2$ .

$\frac{- 2 m}{- 2} = \frac{- 20}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 m}{- 2} = \frac{- 20}{- 2}$

Divide $m$ by $1$ .

$m = \frac{- 20}{- 2}$

Simplify the right side.

Divide $- 20$ by $- 2$ .

$m = 10$