# How do you solve 3(-9m + 9) = 5(-m + 45)?

Jul 14, 2015

$m = - 9$

#### Explanation:

We are given $3 \left(- 9 m + 9\right) = 5 \left(- m + 45\right)$

First let's multiply the $3$ and the $5$ into the parenthesis:

$3 \left(- 9 m + 9\right) = 5 \left(- m + 45\right)$

$3 \cdot \left(- 9 m\right) + 3 \cdot 9 = 5 \cdot \left(- m\right) + 5 \cdot 45$

$- 27 m + 27 = - 5 m + 225$

Let's now add $5 m$ to both sides:

$- 27 m + 27 = - 5 m + 225$

$- 22 m + 27 = 225$

and then, subtract $27$ from both sides:

$- 22 m + 27 = 225$

$- 22 m = 198$

Now, let's divide both sides by $- 22$:

$- 22 m = 198$

$m = - 9$

Let's check our answer by plugging in $- 9$ into $m$:

$3 \left(- 9 m + 9\right) = 5 \left(- m + 45\right)$

$3 \left(- 9 \cdot \left(- 9\right) + 9\right) = 5 \left(- \left(- 9\right) + 45\right)$

$3 \left(81 + 9\right) = 5 \left(54\right)$

$3 \left(90\right) = 270$

$270 = 270$