Algebra 1 · Unit 2
Write inequalities and number lines in interval notation, and read an interval as an inequality.
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Brackets and parentheses
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
A closed dot on a number line is included. An open circle is not.
Infinity
An arrow that does not stop is infinity.
Use a parenthesis next to ∞ and next to −∞.
Write the smaller number on the left.
Two parts
Or makes two separate parts. Join them with ∪.
(−∞, ∞) means every real number.
Write the interval.
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
x ≥ −2
−2 is included. The other end is ∞.
[−2, ∞)
Answer: [−2, ∞)
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
x < 3
3 is not included. The other end is −∞.
(−∞, 3)
Answer: (−∞, 3)
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
−3 < x ≤ 1
−3 is not included. 1 is included.
(−3, 1]
Answer: (−3, 1]
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
x ≤ 5
5 is included. The other end is −∞.
(−∞, 5]
Answer: (−∞, 5]
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
0 ≤ x ≤ 4
0 is included. 4 is included.
[0, 4]
Answer: [0, 4]
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
x > −6
−6 is not included. The other end is ∞.
(−6, ∞)
Answer: (−6, ∞)
Read the circles and the arrows.
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
Open circle at −1. The arrow goes left.
Closed circle at 3. The arrow goes right.
Join the two parts with ∪.
(−∞, −1) ∪ [3, ∞)
Answer: (−∞, −1) ∪ [3, ∞)
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
Closed circle at 2. The arrow goes right.
[2, ∞)
Answer: [2, ∞)
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
Open circle at −4.
Closed circle at 1.
The shading is between them.
(−4, 1]
Answer: (−4, 1]
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
Closed circle at −2. The arrow goes left.
Open circle at 5. The arrow goes right.
Join the two parts with ∪.
(−∞, −2] ∪ (5, ∞)
Answer: (−∞, −2] ∪ (5, ∞)
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
The whole number line is shaded. Both ends go on forever.
(−∞, ∞)
Answer: (−∞, ∞)
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
Open circle at 0. The arrow goes left.
(−∞, 0)
Answer: (−∞, 0)
Write the inequality.
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
[−2, 5)
−2 is included. 5 is not included.
−2 ≤ x < 5
Answer: −2 ≤ x < 5
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
(−∞, 3]
3 is included. The other end is −∞.
x ≤ 3
Answer: x ≤ 3
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
(1, ∞)
1 is not included. The other end is ∞.
x > 1
Answer: x > 1
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
[−4, −1]
−4 is included. −1 is included.
−4 ≤ x ≤ −1
Answer: −4 ≤ x ≤ −1
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
(−∞, 0) ∪ [2, ∞)
0 is not included, and the left part goes forever. 2 is included, and the right part goes forever.
x < 0 or x ≥ 2
Answer: x < 0 or x ≥ 2
Bracket if the endpoint is included. Parenthesis if it is not. Infinity uses a parenthesis.
(−5, 2]
−5 is not included. 2 is included.
−5 < x ≤ 2
Answer: −5 < x ≤ 2
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