# How do you solve 11/3x-1/4=2?

Jan 9, 2017

$x = \frac{27}{44}$

#### Explanation:

Your first goal here is to make sure that all the fractions have the same denominator. As given, the equation looks like this

$\frac{11}{3} x - \frac{1}{4} = \frac{2}{1}$

Now, the common denominator for $3$, $4$, and $1$ is $12$, so you will need to multiply the first fraction by $1 = \frac{4}{4}$, the second fraction by $1 = \frac{3}{3}$, and the third fraction by $1 = \frac{12}{12}$.

This will get you

$\frac{11}{3} x \cdot \frac{4}{4} - \frac{1}{4} \cdot \frac{3}{3} = \frac{2}{1} \cdot \frac{12}{12}$

You now have three fractions with equal denominators

$\frac{11 \cdot 4}{12} x - \frac{1 \cdot 3}{12} = \frac{2 \cdot 12}{12}$

$\frac{44}{12} x - \frac{3}{12} = \frac{24}{12}$

You can now focus exclusively on the numerators and say that

$44 \cdot x - 3 = 24$

Add $3$ to both sides of the equation

$44 \cdot x - \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} = 24 + 3$

$44 \cdot x = 27$

Divide both sides of the equation by $44$ to get

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{44}}} \cdot x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{44}}}} = \frac{27}{44}$

$x = \frac{27}{44}$

Do a quick double-check to make sure that the calculations are correct

$\frac{11}{3} \cdot \frac{27}{44} - \frac{1}{4} = 2$

$\frac{11 \cdot 9}{44} - \frac{1}{4} = 2$

$\frac{9}{4} - \frac{1}{4} = 2$

$\frac{8}{4} = 2 \text{ } \textcolor{\mathrm{da} r k g r e e n}{\sqrt{}}$