# How do you solve 3/5=6/(x+3)?

Jun 23, 2018

See a solution process below:

#### Explanation:

Multiply each side of the equation by $\textcolor{red}{5} \left(\textcolor{b l u e}{x + 3}\right)$ to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{5} \left(\textcolor{b l u e}{x + 3}\right) \times \frac{3}{5} = \textcolor{red}{5} \left(\textcolor{b l u e}{x + 3}\right) \times \frac{6}{x + 3}$

$\cancel{\textcolor{red}{5}} \left(\textcolor{b l u e}{x + 3}\right) \times \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} = \textcolor{red}{5} \cancel{\left(\textcolor{b l u e}{x + 3}\right)} \times \frac{6}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{x + 3}}}}$

$3 \left(\textcolor{b l u e}{x + 3}\right) = \textcolor{red}{5} \times 6$

$\left(3 \times \textcolor{b l u e}{x}\right) + \left(3 \times \textcolor{b l u e}{3}\right) = 30$

$3 x + 9 = 30$

Next, subtract $\textcolor{red}{9}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$3 x + 9 - \textcolor{red}{9} = 30 - \textcolor{red}{9}$

$3 x + 0 = 21$

$3 x = 21$

Now, divide each side of the equation by $\textcolor{red}{3}$ to solve for $x$ while keeping the equation balanced:

$\frac{3 x}{\textcolor{red}{3}} = \frac{21}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = 7$

$x = 7$

Jun 23, 2018

$x = 7$

#### Explanation:

Since we have two fractions on either side of an equal sign, this designates that we can cross multiply here. So, let's multiply $3$ by $x + 3$ and $5$ by $6$.

$3 \left(x + 3\right)$ gives us $3 x + 9$ and $5 \times 6$ gives us $30$. Then we just solve:

$3 x + 9 = 30$

Subtract $9$ from both sides:

$3 x = 21$

Divide by $3$ on both sides:

$x = 7$

Hope this helps!