Chapter 8.7, Problem 60HP

To determine

Write an inequality and name three numbers that are possible solutions.

Answer to Problem 60HP

  $\frac{x}{-5}+4\le 8;x\ge -20;$ The three numbers that are possible solutions are $-18,0,18$

Explanation of Solution

Given:

Write an inequality for the following sentence. The quotient of a number and − 5 increased by 4 is at most 8. Name three numbers that are possible solutions. Explain.

Concept Used:

Translate the sentence into an inequality.

The quotient of a number and − 5 increased by 4 is at most 8.

The required inequality: $\frac{x}{-5}+4\le 8$

Calculation:

The required inequality: $\frac{x}{-5}+4\le 8$

  $\begin{array}{l}\frac{x}{-5}+4\le 8\\ \frac{x}{-5}+4-4\le 8-4\text{[}\text{Subtract}4\text{from}\text{both}\text{sides}\text{]}\\ \frac{x}{-5}\le 4\\ -5·\frac{x}{-5}\ge -5·4[\text{Multiply}\text{both}\text{sides}\text{by}-5\text{and}\text{reverse}\text{the}\text{inequality}\text{]}\\ x\ge -20\end{array}$

So, the numbers must be greater than or equal to − 20 to satisfy the inequality.

Name three numbers that are possible solutions:

  $-18,0,18$ Because they are greater than − 20

Thus, the solution of the inequality $\frac{x}{-5}+4\le 8$ is $x\ge -20$ and three numbers that are possible solutions are $-18,0,18$