# How do you solve 6(m-3)>5(2m+4)?

Feb 11, 2017

See the entire solution process below:

#### Explanation:

First, multiply the terms within parenthesis on each side of the inequality:

$\left(6 \times m\right) - \left(6 \times 3\right) > \left(5 \times 2 m\right) + \left(5 \times 4\right)$

$6 m - 18 > 10 m + 20$

Next, subtract $\textcolor{red}{6 m}$ and $\textcolor{b l u e}{20}$ from each side of the inequality to isolate the $m$ term while keeping the inequality balanced:

$6 m - 18 - \textcolor{red}{6 m} - \textcolor{b l u e}{20} > 10 m + 20 - \textcolor{red}{6 m} - \textcolor{b l u e}{20}$

$6 m - \textcolor{red}{6 m} - 18 - \textcolor{b l u e}{20} > 10 m - \textcolor{red}{6 m} + 20 - \textcolor{b l u e}{20}$

$0 - 38 > 4 m + 0$

$- 38 > 4 m$

Now, divide each side of the inequality by $\textcolor{red}{4}$ to solve for $m$ while keeping the inequality balanced:

$\frac{- 38}{\textcolor{red}{4}} > \frac{4 m}{\textcolor{red}{4}}$

$\frac{2 \times - 19}{2 \times 2} > \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} m}{\cancel{\textcolor{red}{4}}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times - 19}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 2} > \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} m}{\cancel{\textcolor{red}{4}}}$

$- \frac{19}{2} > m$

To solve for $m$ we need to reverse or "flip" the inequality:

$m < - \frac{19}{2}$