Chapter 1.5, Problem 61PPSE

Solution

To solve the compound inequality $15x>30\text{or }18x<-36$ and graph the solution.

  $x<-2\text{or }x>2$

The graph of solution set is shown below:

  

Given:

The compound inequality, $15x>30\text{or }18x<-36$ .

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:

In order to solve the given inequality $15x>30\text{or }18x<-36$ , perform the basic algebraic operations to isolate the variable term as shown below

  $\begin{array}{c}15x>30\text{or }18x<-36\\ \frac{15x}{15}>\frac{30}{15}\text{or }\frac{18x}{18}<\frac{-36}{18}\\ x>2\text{or }x<-2\end{array}$

Thus, the solution of the given inequality is $x<-2\text{or }x>2$ .

Since the inequality sign is strict with both endpoints, use the solid circles at both endpoints and shade the region to the left of $-2$ and to the right side of 2 as shown below