When solving linear inequalities in one variable, the solution is often a range of numbers or an interval. To display an interval, we have a special type of notation, known as interval notation. We can also use set builder notation or graph the interval using a number line.
Test Objectives:•Demonstrate the ability to write an interval using interval notation
•Demonstrate the ability to write an interval using set builder notation
•Demonstrate the ability to graph an interval on a number line
Interval Notation Test:
#1:
Instructions: Write each in interval notation, set builder notation, and graph the interval.
a) x ≥ 9
#2:
Instructions: Write each in interval notation, set builder notation, and graph the interval.
a) x < -7
#3:
Instructions: Write each in interval notation, set builder notation, and graph the interval.
a) x > 2
#4:
Instructions: Write each in interval notation, set builder notation, and graph the interval.
a) -9 ≤ x ≤ 9
#5:
Instructions: Write each in interval notation, set builder notation, and graph the interval.
a) -4 < x ≤ 2
Written Solutions:
Solution:
a) [9, ∞) - interval notation
{x | x ≥ 9} - set builder notation
Solution:
a) (-∞, -7) - interval notation
{x | x < -7} - set builder notation
Solution:
a) (2, ∞) - interval notation
{x | x > 2} - set builder notation
Solution:
a) [-9, 9] - interval notation
{x | -9 ≤ x ≤ 9} - set builder notation
Solution:
a) (-4, 2] - interval notation
{x | -4 < x ≤ 2} - set builder notation