Exercise 6 Page 40

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 ≥ 4or m ≤ -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. (- ∞,- 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, + ∞) Finally, note that the given exercise says m≥ 4 or m≤ - 7. This means that the solution set is the union of the intervals. (- ∞,- 7 ] ⋃ [ 4, +∞)