Question

Solve$\frac{1}{5}\left(n+3\right)=\frac{1}{4}\left(n+2\right)$

Short answer

The answer is$n=2$

Step-by-step solution

Step 1. Given information

The equation is $\frac{1}{5}\left(n+3\right)=\frac{1}{4}\left(n+2\right)$.

Find value of n.

Step 2. Calculation

Simplify the equation $\frac{1}{5}\left(n+3\right)=\frac{1}{4}\left(n+2\right)$

LCD of 5,4 is 20.

so, $20\left(\frac{1}{5}\left(n+3\right)\right)=20\left(\frac{1}{4}\left(n+2\right)\right)$

Simplify the equation

$$\begin{gathered} 4\left(n+3\right)=5\left(n+2\right) \\ 4n+12=5n+10 \end{gathered}$$

combine like terms

$$\begin{gathered} 12-10=5n-4n \\ 2=n \end{gathered}$$