# How do you solve 3y + 1/2 = 4 + 2/3 y?

##### 1 Answer
May 24, 2015

First subtract $\frac{1}{2}$ from both sides to get:

$3 y = \frac{7}{2} + \frac{2}{3} y$

Subtract $\frac{2}{3} y$ from both sides to get:

$\frac{7}{3} y = \frac{7}{2}$

Multiply both sides by $\frac{3}{7}$ to get:

$y = \frac{3}{2}$

Check by substituting this value back into the original equation:

LHS $= 3 y + \frac{1}{2} = 3 \left(\frac{3}{2}\right) + \frac{1}{2} = \frac{9}{2} + \frac{1}{2} = \frac{10}{2} = 5$

RHS $= 4 + \frac{2}{3} y = 4 + \left(\frac{2}{3} \cdot \frac{3}{2}\right) = 4 + 1 = 5$