Example 1: x > −3 and x ≤ 4
The solution set, shown in the bottom graph, is {x| -3 < x ≤ 4}
Remember that open circles denote < and > while solid circles denote ≤ and ≥.
Example 2: t ≥ 8 or t < 5.
The solution set is {t| t ≥ 8 or t < 5}
Sometimes it is better to first solve each inequality and then graph the solution. Study the examples below.
Example 3: −3 ≤ p − 5 < 2
Both "sides" of this compound inequality must be true, so the solution is their intersection.
−3 ≤ p − 5 −3 + 5 ≤ p − 5 + 5 2 ≤ p |
p − 5 < 2
p − 5 + 5 < 2 + 5 p < 7 |
The solution set is {p| 2 ≤ p < 7} |
Example 4: 2a + 1 < 11 or a > 3a + 2
The solution to this compound inequality is the union of the solutions to each "side."
2a + 1 < 11 2a + 1 − 1 < 11 − 1 2a < 10 a < 5 |
a > 3a + 2 a − 3a > 3a − 3a + 2 −2a > 2 −2a ÷ −2 > 2 ÷ −2 a < −1 |
The solution set is {a| a < 5} |
