Chapter SH, Problem 5.5.18EP

To determine

The solution of the given inequality

Answer to Problem 5.5.18EP

  $n\ge 1.62$

Explanation of Solution

Given:

The given inequality is

  $\frac{3(n+1)}{7}\ge \frac{n+4}{5}$

Calculation:

The given inequality can be solved as

  $\begin{array}{l}\frac{3(n+1)}{7}\ge \frac{n+4}{5}\\ \frac{3n+3}{7}\ge \frac{n+4}{5}\\ 5\left(3n+3\right)\ge 7(n+4)\\ 15n+15\ge 7n+28\\ 15n-7n\ge 28-15\\ 8n\ge 13\\ n\ge \frac{13}{8}\\ n\ge 1.62\end{array}$

Check: Put n = 1.5, to check,

  $\begin{array}{l}\frac{3(n+1)}{7}\ge \frac{n+4}{5}\\ \frac{3(1.5+1)}{7}\ge \frac{1.5+4}{5}\\ \frac{3(2.5)}{7}\ge \frac{5.5}{5}\\ \frac{7.5}{7}\ge 1.1\\ 1.07\ge 1.1\\ \text{which is not possible}\text{.}\\ \text{Hence, n}\ge 1.62\end{array}$