How do you solve -5(m-1)+3(2m-1)=8 using the distributive property?

Apr 24, 2017

See the entire solution process below:

Explanation:

First, expand both terms in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{- 5} \left(m - 1\right) + \textcolor{b l u e}{3} \left(2 m - 1\right) = 8$

$\left(\textcolor{red}{- 5} \cdot m\right) + \left(\textcolor{red}{- 5} \cdot - 1\right) + \left(\textcolor{b l u e}{3} \cdot 2 m\right) - \left(\textcolor{b l u e}{3} \cdot 1\right) = 8$

$- 5 m + 5 + 6 m - 3 = 8$

Next, group and combine like terms on the left side of the equation:

$6 m - 5 m + 5 - 3 = 8$

$\left(6 - 5\right) m + \left(5 - 3\right) = 8$

$1 m + 2 = 8$

$m + 2 = 8$

Now, subtract $\textcolor{red}{2}$ from each side of the equation to solve for $m$ while keeping the equation balanced:

$m + 2 - \textcolor{red}{2} = 8 - \textcolor{red}{2}$

$m + 0 = 6$

$m = 6$