# How do you solve x/2 + x/3 - 1 = x/6 + 3?

Feb 2, 2016

$\left(\frac{x}{2} \cdot \frac{3}{3}\right) + \left(\frac{x}{3} \cdot \frac{2}{2}\right) - \frac{x}{6} = 4 \rightarrow \frac{4 x}{6} = 4$, therefore, $x = 6$

#### Explanation:

To add and subtract fractions they must have a common denominator. The common denominator for $2 , 3$ and $6$ is $6$, therefore $\frac{x}{2}$ is multiplied by $\frac{3}{3}$ (any number over itself = $1$, so you are not changing the value of the fraction by multiplying it by $1$) and $\frac{x}{3}$ is multiplied by $\frac{2}{2}$, resulting in $\frac{3 x}{6} + \frac{2 x}{6}$, which equals $\frac{5 x}{6}$. Now we move all of the fractions to one side of the equation and the whole numbers to the other:

$\frac{5 x}{6} - \frac{x}{6} - 1 + 1 = \frac{x}{6} - \frac{x}{6} + 1 + 3$

$= \frac{4 x}{6} = 4$

$6 \cdot 4 = 4 x$, therefore, $x = 6$

Feb 2, 2016

$\frac{x}{2} + \frac{x}{3} - 1 = \frac{x}{6} + 3$

$\rightarrow \frac{3 x + 2 x}{6} - 1 = \frac{x}{6} + 3$

$\rightarrow \frac{5 x}{6} - 1 = \frac{x}{6} + 3$

$\rightarrow \frac{5 x}{6} = \frac{x}{6} + 3 + 1$

$\rightarrow \frac{5 x}{6} = \frac{x}{6} + 4$

$\rightarrow \frac{5 x}{6} - \frac{x}{6} = 4$

$\rightarrow \frac{4 x}{6} = 4$

$\rightarrow \frac{2 x}{3} = 4$

$\rightarrow 2 x = 4 \cdot 3$

$\rightarrow 2 x = 12$

$\rightarrow x = \frac{12}{2} = 6$