Chapter 8.8, Problem 29E

To determine

To solve:

The given inequality.

Answer to Problem 29E

The solution for our given inequality would be $y\le 7$ and in interval notation $(-\infty ,7]$ .

Explanation of Solution

Given:

An inequality:

  $y-5\le 2$ .

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:

  $\begin{array}{l}y-5\le 2\text{(Given inequality)}\\ y-5+5\le 2+5(\text{Adding }5\text{on both sides)}\\ y\le 7\end{array}$

Therefore, the solution for our given inequality would be all values of yless than or equal to7. The solution of our given inequality in interval notation would be $(-\infty ,7]$ .

Since 7is a solution of our given inequality, so we will have a solid dot at $y=7$ . Upon graphing solution of our given inequality, we will get: