# How do you solve 5/9x+3=2/3?

Feb 1, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{9}$ to eliminate the fraction while keeping the equation balanced. Eliminating the fraction will make the problem easier to work with.

$\textcolor{red}{9} \left(\frac{5}{9} x + 3\right) = \textcolor{red}{9} \times \frac{2}{3}$

$\left(\textcolor{red}{9} \times \frac{5}{9} x\right) + \left(\textcolor{red}{9} \times 3\right) = \cancel{\textcolor{red}{9}} 3 \times \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}$

$\left(\cancel{\textcolor{red}{9}} \times \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}}} x\right) + 27 = 6$

$5 x + 27 = 6$

Next, subtract $\textcolor{red}{27}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$5 x + 27 - \textcolor{red}{27} = 6 - \textcolor{red}{27}$

$5 x + 0 = - 21$

$5 x = - 21$

Now, divide each side of the equation by $\textcolor{red}{5}$ to solve for $x$ while keeping the equation balanced:

$\frac{5 x}{\textcolor{red}{5}} = - \frac{21}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = - \frac{21}{5}$

$x = - \frac{21}{5}$

Feb 1, 2017

$x = - \frac{21}{5}$

#### Explanation:

A fraction consists of: " "("count")/("size indicator") -> ("numerator")/("denominator")

You can not directly subtract or add the counts (numerators) unless the size indicators (denominators) are the same.

color(green)((5x)/9+[3color(red)(xx1)]=2/3color(red)(xx1)

color(green)((5x)/9+[3color(red)(xx9/9)]=2/3color(red)(xx3/3)

$\textcolor{g r e e n}{\frac{5 x}{9} + \left[\frac{27}{9}\right] = \frac{6}{9}}$

As all the denominators (size indicators) are the same it is equally true that:

$5 x + 27 = 6$

Subtract 27 from both sides

$5 x = - 21$

Divide both sides by 5

$x = - \frac{21}{5}$