Chapter 1.5, Problem 13PPSE

Solution

To write an inequality for the given sentence.

  $\frac{x}{12}\le 6$

Given:

The quotient of a number and 12 is no more than 6.

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 quotient of a number x and 12 is no more than 6, the quotient of the number and 12 must be less than or equal to 6. It can be expressed in inequality form as

  $\begin{array}{l}x÷12\le 6\\ \frac{x}{12}\le 6\end{array}$

Thus, the inequality that represent the given sentence is $\frac{x}{12}\le 6$ .