Chapter 3.6, Problem 29PPE

To determine

To write: The inequality $x<-2$ or $x\ge 1$ in interval notation. Then graph the solutions.

Answer to Problem 29PPE

The inequality $x<-2$ or $x\ge 1$ can be expressed in interval notation as $\left(-\infty ,-2\right)\cup \left[1,\infty \right)$ .

Explanation of Solution

Given information: The inequality is $x<-2$ or $x\ge 1$ .

Calculation:

From the inequality $x<-2$ or $x\ge 1$ , it is observed that the symbol $\ge$ indicates that the number 1 is included and the symbol $<$ indicates that the number $-2$ is not included.

So, the inequality $x<-2$ or $x\ge 1$ can be expressed in interval notation as $\left(-\infty ,-2\right)\cup \left[1,\infty \right)$ .

Graph the interval $\left(-\infty ,-2\right)\cup \left[1,\infty \right)$ on the number line as shown below in Figure 1.

  

Figure 1

Thus, the inequality $x<-2$ or $x\ge 1$ can be expressed in interval notation as $\left(-\infty ,-2\right)\cup \left[1,\infty \right)$