# How do you solve 4x+16=8x-32?

Dec 30, 2016

See explanation below on how to solve this problem:

#### Explanation:

Step 1) Add the necessary values to 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:

$4 x + 16 - \textcolor{red}{4 x} + \textcolor{b l u e}{32} = 8 x - 32 \textcolor{red}{-} \textcolor{red}{4 x} + \textcolor{b l u e}{32}$

Group and combine like terms on each side of the equation:

$4 x - \textcolor{red}{4 x} + 16 + \textcolor{b l u e}{32} = 8 x - \textcolor{red}{4 x} - 32 \textcolor{red}{+} \textcolor{b l u e}{32}$

$0 + 16 + 32 = 8 x - 4 x - 0$

$48 = 4 x$

Now we can divide each side of the equation by $\textcolor{red}{4}$ to solve for $x$ while keeping the equation balanced:

$\frac{48}{\textcolor{red}{4}} = \frac{4 x}{\textcolor{red}{4}}$

$12 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}}$

$12 = x$

$x = 12$