Chapter A, 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.

Explanation of Solution

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

From the given set, observe that the value of x will not satisfy the point $-4$ and satisfies the point 10 as the given set is half opened.

Also, note that x satisfies all the points to the right of $-4$ and to the left from the point 10.

Thus, the given set can be expressed in the interval notation as $\left(-4,10\right]$.

Plot the given set in the form of a number line as shown below.

From Figure 1, it can be concluded that the dark shaded region is the region of the given set.