A shorthand for writing all real numbers in a range, using parentheses for excluded endpoints and square brackets for included endpoints.
Parentheses mean the endpoint is NOT included; square brackets mean it IS included. For example, (2,5] means 2<x≤5.
Showing a random 20 of 50 problems.
Example 1
challenge
Solve x+1x2−4≥0 and write the solution in interval notation.
Example 2
medium
Write the domain of f(x)=x−4 in interval notation.
Example 3
challenge
Solve ∣x−1∣+∣x+2∣≤5 and write the solution in interval notation.
Example 4
medium
Convert the interval [0,4) to inequality notation.Read off the inequality: [0, 4) → bracket at 0 means ≥, parenthesis at 4 means <
Example 5
medium
Write the domain of f(x)=2x−6 in interval notation.
Example 6
medium
Write the set of x with 0≤x≤10 excluding x=5 in interval notation.
Example 7
hard
Solve ∣2x−3∣<5 and write the solution in interval notation.
Example 8
easy
Convert the interval [0,∞) back to an inequality.
Example 9
medium
Solve 3x−5≤7 and write the solution in interval notation.
Example 10
medium
Write the union [1,4]∪[3,7] as a single interval.
Example 11
medium
Convert (−∞,−1]∪[4,∞) to an inequality statement.
Example 12
easy
Write 2<x<7 in interval notation.Both endpoints open (excluded); all values strictly between 2 and 7
Example 13
easy
Write 1≤x≤4 in interval notation.Filled dots at both ends; the closed interval includes every point from 1 to 4
Example 14
medium
Solve 5−2x>1 and write the solution in interval notation.
Example 15
easy
Convert (−2,5] to an inequality.Open at −2 (excluded, <); filled at 5 (included, ≤)
Example 16
medium
Write the solution of 5−2x≥1 in interval notation.
Example 17
easy
Write x≥−2 in interval notation.Filled dot at −2 (≥ includes it); bracket in interval notation becomes a filled circle on the number line
Example 18
medium
Express the intersection of [1,5] and [3,8] in interval notation.[1, 5] ∩ [3, 8] = [3, 5]: the overlap runs from the larger left end to the smaller right end
Example 19
challenge
Write the solution set of x2≤9 in interval notation.x² ≤ 9 means −3 ≤ x ≤ 3; both endpoints included because equality holds at x
Example 20
medium
Express 'numbers from −1 to 6, excluding 3' in interval notation.