# How do you solve (2x+1)(1/3)=3 and find any extraneous solutions?

May 2, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{3}$ to eliminate the fraction while keeping the equation balanced:

$\left(2 x + 1\right) \left(\frac{1}{3}\right) \times \textcolor{red}{3} = 3 \times \textcolor{red}{3}$

$\left(2 x + 1\right) \left(\frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}\right) \times \cancel{\textcolor{red}{3}} = 9$

$2 x + 1 = 9$

Next, subtract $\textcolor{red}{1}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$2 x + 1 - \textcolor{red}{1} = 9 - \textcolor{red}{1}$

$2 x + 0 = 8$

$2 x = 8$

Now, divide each side of the equation by $\textcolor{red}{2}$ to solve for $x$ while keeping the equation balanced:

$\frac{2 x}{\textcolor{red}{2}} = \frac{8}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = 4$

$x = 4$

There are no extraneous solutions.