Question

Write interval notation for the sets of x's described by the inequalities below:

a. X < 4
b. X ≥ 0
c. 0 < X ≤ 5
d. -2 ≤ X < 1
e. 0 < X < 1
f. -2 ≤ X ≤ 5

Answer 1

Interval notation translates inequalities into a form that specifies the endpoints of the interval and whether these endpoints are included in the set. Parentheses indicate exclusion, and brackets indicate inclusion. An example is X < 4, which in interval notation is written as (-infinity, 4).

Step-by-step explanation:

Writing interval notation for the sets of x's described by the following inequalities:

• a. For X < 4, the interval notation is (-∞, 4).
• b. For X ≥ 0, the interval notation is [0, ∞).
• c. For 0 < X ≤ 5, the interval notation is (0, 5].
• d. For -2 ≤ X < 1, the interval notation is [-2, 1).
• e. For 0 < X < 1, the interval notation is (0, 1).
• f. For -2 ≤ X ≤ 5, the interval notation is [-2, 5].

In interval notation, we use parentheses to indicate that an endpoint is not included (open interval) and brackets to indicate that an endpoint is included (closed interval). An infinity symbol (∞) is used to denote unboundedness in one direction, and it is always used with parentheses, as there's no defined endpoint at infinity.