# How do you solve \frac { 7} { 2} x + 3= \frac { 1} { 2} + \frac { 1} { 2} x?

Oct 19, 2017

The answer is $x = - \frac{5}{6}$

#### Explanation:

The first step is to combine like terms.

The $\frac{1}{2} x$ would move to the left side of the equal sign. You also have to change the sign, basically you have to subtract since the sign is "+":

$\left(\frac{7}{2} x - \frac{1}{2} x\right) + 3 = \frac{1}{2}$

$\left(\frac{6}{2} x\right) + 3 = \frac{1}{2}$

You would also combine the terms without the $x$.

$\frac{6}{2} x = \left(\frac{1}{2} - 3\right)$

$\frac{6}{2} x = - \frac{5}{2}$

We can simplify $\frac{6}{2} x$ to $3 x$.

The next step is to multiply each side of the equation with the reciprocal to get rid of the $3$.

$\left(\frac{1}{3}\right) \cdot 3 x = - \frac{5}{2} \cdot \left(\frac{1}{3}\right)$

$x = - \frac{5}{6}$