# How do you solve 1/5 + (3x)/15=4/5?

Aug 26, 2015

$x = 3$

#### Explanation:

Your ultimate goal is to isolate $x$ on one side of the equation, so start by getting rid of the denominators.

Notice that you can multiply $\frac{1}{5}$ and $\frac{4}{5}$ by $1 = \frac{3}{3}$ to get

$\frac{1}{5} \cdot \frac{3}{3} + \frac{3 x}{15} = \frac{4}{5} \cdot \frac{3}{3}$

$\frac{3}{15} + \frac{3 x}{15} = \frac{12}{15}$

All the terms have the same denominator, which means that you can write

$\frac{3 + 3 x}{15} = \frac{12}{15}$

$\left(3 + 3 x\right) \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{\frac{1}{15}}}} = 12 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{\frac{1}{15}}}}$

$3 + 3 x = 12$

Next, add $- 3$ to both sides of the equation

$\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} + 3 x = 12 - 3$

$3 x = 9$

Finally, divide both sides by $3$ to get $x$ alone on the left-hand side of the equation

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \frac{9}{3}$

$x = \textcolor{g r e e n}{3}$