Chapter 1.5, Problem 14PPSE

Solution

To solve the inequality $-12\ge 24x$ and graph the solution.

  $x\le -\frac{1}{2}$

The graph of solution set is shown below:

  

Given:

The inequality, $-12\ge 24x$ .

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 $-12\ge 24x$ , perform the basic algebraic operations to isolate the variable term as shown below

  $\begin{array}{c}-12\ge 24x\\ \frac{-12}{24}\ge \frac{24x}{24}\\ -\frac{1}{2}\ge x\\ x\le -\frac{1}{2}\end{array}$

Thus, the solution of the given inequality is $x\le -\frac{1}{2}$ .

Since the inequality sign is not strict, use a solid circle at $-\frac{1}{2}$ and move toward left on the number line as shown below