Answer
$n\geq 18$
Work Step by Step
Given \begin{equation}
\begin{aligned}
\frac{1}{4} n+3 \leq \frac{2}{5} n+\frac{3}{10}.
\end{aligned}
\end{equation} Rewrite the inequality so that the variable, $n$ is on the left side of the inequality sign. Change the direction of the inequality sign if you divide or multiply by a negative number.
\begin{equation}
\begin{aligned}
\frac{1}{4} n+3 &\leq \frac{2}{5} n+\frac{3}{10}\\
\left(\frac{1}{4} n+3\right)\cdot 20 &\leq\left( \frac{2}{5} n+\frac{3}{10}\right)\cdot 20\\
5n+60&\leq 8n+ 6\\
5n-8n&\leq 6-60\\
-3n&\leq - 54\\
n&\geq \frac{-54}{-3}\\
n &\geq 18.
\end{aligned}
\end{equation} The solution is $n\geq 18$.
