# How do you solve 3/5 (x-12) >x-24?

##### 1 Answer
Feb 11, 2017

See the entire solution process below:

#### Explanation:

First, expand the term in parenthesis on the left side of the inequality:

$\left(\frac{3}{5} \times x\right) - \left(\frac{3}{5} \times 12\right) > x - 24$

$\frac{3}{5} x - \frac{36}{5} > x - 24$

Next, subtract $\textcolor{red}{\frac{3}{5} x}$ and add $\textcolor{b l u e}{24}$ to each side of the inequality while keeping the inequality balanced:

$\frac{3}{5} x - \frac{36}{5} - \textcolor{red}{\frac{3}{5} x} + \textcolor{b l u e}{24} > x - 24 - \textcolor{red}{\frac{3}{5} x} + \textcolor{b l u e}{24}$

$\frac{3}{5} x - \textcolor{red}{\frac{3}{5} x} - \frac{36}{5} + \textcolor{b l u e}{24} > x - \textcolor{red}{\frac{3}{5} x} - 24 + \textcolor{b l u e}{24}$

$0 - \frac{36}{5} + \left(\frac{5}{5} \times \textcolor{b l u e}{24}\right) > \left(\frac{5}{5} \times x\right) - \textcolor{red}{\frac{3}{5} x} - 0$

$- \frac{36}{5} + \frac{120}{5} > \frac{5}{5} x - \frac{3}{5} x$

$\frac{84}{5} > \frac{2}{5} x$

Now, multiply each side of the equation by color(red)(5)/color(2) to solve for $x$ while keeping the equation balanced:

$\frac{\textcolor{red}{5}}{\textcolor{b l u e}{2}} \times \frac{84}{5} > \frac{\textcolor{red}{5}}{\textcolor{b l u e}{2}} \times \frac{2}{5} x$

$\frac{\cancel{\textcolor{red}{5}}}{\textcolor{b l u e}{2}} \times \frac{84}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} > \frac{10}{10} x$

$\frac{84}{2} > 1 x$

$42 > x$

Finally, to solve in terms of $x$ we need to reverse or "flip" the inequality:

$x < 42$