Chapter 1.5, Problem 11PPSE

Solution

To write an inequality for the given sentence.

  $8x\ge 25$

Given:

The product of a number and 8 is at least 25.

Concept Used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval
• To graph the endpoint with strict inequality $<\text{ or}>$ , use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$ , use the bracket or a solid circle at that endpoint.
• Multiplying or dividing an inequality by a negative number reverse the inequality sign.

Calculation:

Let x represent the unknown number.

Since the product of the number x and 8 is at least 25, the product of the number and 8 must be greater than or equal to 25. It can be expressed in inequality form as

  $\begin{array}{l}x\cdot 8\ge 25\\ 8x\ge 25\end{array}$

Thus, the inequality that represent the given sentence is $8x\ge 25$ .