We want to write the given inequality using interval notation. In interval notation, a square bracket means that the stated value is in the set and a parenthesis means that every value up to but not including the stated value is in the set. Infinity always gets a parenthesis because nothing can ever reach infinity. Let's begin by interpreting the given set-builder notation.

{m ∣ m \geq 4 or m \leq - 7} m is greater than or equal to 4 or m is less than or equal to - 7

We can also represent the inequality on a number line.

Let's consider the intervals one at a time, starting with the left-hand side. Since

- 7

is included in the solution, we will use a bracket. The set is unbounded in the negative direction, so we will use negative infinity with a parenthesis.

(- \infty, - 7]

Looking at the inequality on the right-hand side, we can see that

4

is included so we will use a bracket. The set is unbounded in the positive direction, so we will use infinity with a parenthesis.

[4, + \infty)

Finally, note that the given exercise says

m \geq 4

or

m \leq - 7 .

This means that the solution set is the union of the intervals.

(- \infty, - 7] \cup [4, + \infty)

Exercise