Answer
\[x=\frac{2}{5}\]
Work Step by Step
\[\frac{x+2}{3}=\frac{4}{5}\]
The LCM is\[15\] so multiply both the sides by \[15\]
\[\frac{x+2}{3}\times 15=\frac{4}{5}\times 15\]
This gives,
\[5\left( x+2 \right)=12\]
Apply the distributive law
\[5x+10=12\]
Or,
\[5x=2\]
Divide both the sides by \[5\]
\[x=\frac{2}{5}\]
Now, to check it, put \[x=\frac{2}{5}\]in the equation
\[\begin{align}
& \frac{x+2}{3}=\frac{4}{5} \\
& \frac{\frac{2}{5}+2}{3}=\frac{4}{5} \\
& \frac{12}{15}=\frac{4}{5} \\
& \frac{4}{5}=\frac{4}{5} \\
\end{align}\]
which is true.
The required solution is\[x=\frac{2}{5}\].
