Chapter 1.5, Problem 52PPSE

Solution

The compound inequality that shows the pH levels of the shampoo.

  $x\ge 6.0\text{ and }x\le 6.5$

  

Given:

The pH level of a popular shampoo is between 6.0 and 6.5 inclusive.

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.
• Average is the quotient of the sum of all data points and the number of data points.

Calculation:

Let x be the pH level of the shampoo.

Since the pH level of the shampoo is between 6.0 and 6.5inclusive, the pH level must be greater than or equal to 6.0 and less than or equal to 6.5.

Thus, the compound inequality that represents the pH level of the shampoo is $x\ge 6.0\text{ and }x\le 6.5$ .

The graph of the compound inequality is shown below: