Chapter 8.8, Problem 31E

To determine

To solve:

The given inequality.

Answer to Problem 31E

The solution for our given inequality would be $n<12$ and in interval notation $(-\infty ,12)$ .

Explanation of Solution

Given:

An inequality:

  $\frac{n}{2}<6$ .

Concept used:

To solve an inequality, we use opposite operations as we use to solve an equation. When we divide or multiply both sides of an inequality by any negative number, it reverses the inequality.

Calculation:

We will solve our given inequality using opposite operations as shown below:

  $\begin{array}{l}\frac{n}{2}<6\text{(Given inequality)}\\ \frac{n}{2}\cdot 2<6\cdot 2(\text{Multiplying both sides by }2\text{)}\\ n<12\end{array}$

Therefore, the solution for our given inequality would be all values of nless than $12$ . The solution of our given inequality in interval notation would be $(-\infty ,12)$ .

Since 12isnot a solution of our given inequality, so we will have anopen dot at $n=12$ . Upon graphing solution of our given inequality, we will get: