Chapter B, Problem 1E

State the meaning of {x: –4 < x ≤ 10}. Express the set {x: –4 < x ≤ 10} using interval notation and draw it on a number line.

To determine

To state: The meaning of the given set.

Answer to Problem 1E

The interval notation of the given set is $\left(-4,10\right]$.

Explanation of Solution

Given:

The set is $\left\{x:-4<x\le 10\right\}$.

Meaning:

The given set denotes all those points in the number line which is present in the right of the point $-4$ that is points greater than $-4$ and the points present in the left of 10 that is points less than or equal to 10.

Thus, the interval notation of the given set is $\left(-4,10\right]$.

The set can be plotted in the number line as given below in Figure 1

From Figure 1, it is observed that the darken region is the set given.