Chapter 1.5, Problem 41PPSE

Solution

To solve the compound inequality $3x\ge 3\text{ or }9x<54$ and graph the solution.

All real numbers

Given:

The compound inequality, $3x\ge 3\text{ or }9x<54$ .

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 $3x\ge 3\text{ or }9x<54$ , perform the basic algebraic operations to isolate the variable term as shown below

  $\begin{array}{c}3x\ge 3\text{or }9x<54\\ \frac{3x}{3}\ge \frac{3}{3}\text{or }\frac{9x}{9}<\frac{54}{9}\\ x\ge 1\text{or }x<6\\ \Rightarrow \text{All real numbers}\end{array}$

Thus, the solution of the given inequality is all real number.