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

Oct 4, 2016

$x = \frac{12}{7}$

#### Explanation:

The LCM (lowest common multiple) of 3 and 4 is 12.

Multiplying $\textcolor{b l u e}{\text{All}}$ terms on both sides of the equation by 12 will eliminate the fractions.

${\cancel{12}}^{4} \times \frac{x}{\cancel{3}} ^ 1 + {\cancel{12}}^{3} \times \frac{x}{\cancel{4}} ^ 1 = \left(1 \times 12\right)$

which simplifies to.

$4 x + 3 x = 12 \Rightarrow 7 x = 12$

To solve for x divide both sides by 7.

$\frac{\cancel{7} x}{\cancel{7}} = \frac{12}{7}$

$\Rightarrow x = \frac{12}{7} \text{ is the solution}$