# How do you solve 3x+15=8x-24?

Dec 30, 2016

see explanation below for how to solve this problem:

#### Explanation:

First, add and subtract the necessary values from each side of the equation to isolate the $x$ terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

$3 x + 15 - \textcolor{red}{3 x} + \textcolor{b l u e}{24} = 8 x - 24 - \textcolor{red}{3 x} + \textcolor{b l u e}{24}$

Now group and combine like terms:

$3 x - \textcolor{red}{3 x} + 15 + \textcolor{b l u e}{24} = 8 x - \textcolor{red}{3 x} - 24 + \textcolor{b l u e}{24}$

$0 + 15 + 24 = 8 x - 3 x - 0$

$39 = 5 x$

Now, divide each side of the equation by $\textcolor{red}{5}$ to solve for $x$ and keep the equation balanced:

$\frac{39}{\textcolor{red}{5}} = \frac{5 x}{\textcolor{red}{5}}$

$\frac{39}{5} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}}$

$\frac{39}{5} = x$

$x = \frac{39}{5}$

or

$x = 7.8$