# How do you solve (3x)/9+1/2=x/4+2 and check for extraneous solutions?

Sep 27, 2016

$x = 18$

#### Explanation:

$\frac{3 x}{9} + \frac{1}{2} = \frac{x}{4} + 2 \text{ } \leftarrow$ multiply by the LCM of 36

$\frac{{\textcolor{red}{\cancel{36}}}^{4} \times 3 x}{\cancel{9}} + \frac{{\textcolor{red}{\cancel{36}}}^{18} \times 1}{\cancel{2}} = \frac{{\textcolor{red}{\cancel{36}}}^{9} \times x}{\cancel{4}} + \textcolor{red}{36} \times 2 \text{ } \leftarrow$ cancel

$12 x + 18 = 9 x + 72 \text{ } \leftarrow$ no fractions!

$12 x - 9 x = 72 - 18$

$3 x = 54$

$x = 18$

This is a linear equation. There are no extraneous solutions.