Interval Notation

Closed Intervals: Less than or equal to, or greater than or equal to (≤, ≥)If there are two real numbers a and b, then a ≤ x ≤ b means that the numbers represented by x arebetween a and b, where a is smaller than b, and the values of x can equal a or b.On the number line, there are closed circles at a and b and the line is shaded between them.Interval notation uses brackets [ ] to show the closed circles; the numbers in the parentheses representthe ends of the shaded area.a ≤ x ≤ b ⇒ Interval notation: [a, b] abx ≤ a means that the numbers represented by x are less than or equal to a. This interval includesnumbers from negative infinity ( − ∞)up to and including a.On the number line, there is a closed circle at a and the number line is shaded to the left.Interval notation uses a parenthesis before − ∞ and a bracket after the number a to show the closedcircle.x ≤ a ⇒ Interval notation: ( − ∞,a]ax ≥ b means that the numbers represented by x are greater than or equal to b. This interval includesnumbers from b (and including b) through positive infinity ( ∞ ).On the number line, there is a closed circle at b and the number line is shaded to the right.Interval notation uses a bracket before the number b to show the closed circle and a parenthesis to theright of ∞ .x ≥ b ⇒ Interval notation: [b, ∞) bEx:x ≥ 10 ⇒ Interval notation: [ 10 ,∞)10–5 ≤ x ≤ –3 ⇒ Interval notation: [–5, –3] –5 –3x ≤ 4 ⇒ Interval notation: ( − ∞,4]4