Interval Notation Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Write โˆ’2โ‰คx<5-2 \leq x < 5 in interval notation.

Solution

  1. 1
    Recall interval notation: square brackets [[ or ]] mean the endpoint is included; parentheses (( or )) mean it is excluded.
  2. 2
    Since xโ‰ฅโˆ’2x \geq -2, use a square bracket at โˆ’2-2 (included). Since x<5x < 5, use a parenthesis at 55 (excluded).
  3. 3
    Write the interval: [โˆ’2,5)[-2, 5).

Answer

[โˆ’2,5)[-2, 5)
A half-open interval uses a bracket on the included end and a parenthesis on the excluded end. โ‰ค\leq gets a bracket; << gets a parenthesis.

About Interval Notation

A shorthand for writing all real numbers in a range, using parentheses for excluded endpoints and square brackets for included endpoints.

Learn more about Interval Notation โ†’

More Interval Notation Examples