Name: __________________________________
Aim: Set Builder and Interval Notation
Description
Open to infinity: x > a
Closed to infinity: x ≥ a
Infinity to open: x < a
Infinity to closed: x ≤ a
Graph
Remember…when graphing
Open Circle: < or > (Exclusive)
Closed Circle:  or  (Inclusive)
Interval
Notation
Ex1:
Inequality
Number Line Graph
Interval
Notation
x<4
“x is less than 4”
x>-2
“x is greater than -2”
x ≤ -1
“x is less than or equal to -1”
x  0
“x is greater than or equal to
0”
Ex2: Write the set of all numbers greater than 5 inclusive in interval notation?
Set Builder Notation
x   | x  4
Ex3: For the graph below, write:
A) Inequality: __________________
B) Interval Notation: __________________
-3
-2
C) Set Builder Notation: ________________
Ex4:
a. Solve for x and graph the solution on the number line:
2x < 8
b. Write the inequality in interval notation.
c. Write the inequality in set builder notation.
-1
0
1
2
3
1. Mary wants to buy a new sweater that costs $27. She is paid $9 per hour at her job. She
needs to work at least how many hours to afford the sweater? Express your answer in both
interval and set builder notation.
2. After solving an inequality on your test, you find that the set of answers is all numbers less
than 14. Express your answer in both interval and set builder notation.
3. Keith has $500 in his savings account for the summer. He wants to have at least $200 left
at the end of the summer. If he takes out $25 per week, how many weeks can he make
withdrawals? Express your answer in interval and set notation.
4. Xavier is trying to set the school record for rushing yards in a single season on the football
team. In the final game of the season, he needs to run more than 112 yards to attain his
goal. Express this in both interval and set builder notation.
Name: ____________________________________ Date: ______________ Period: _____
CC Algebra HW: Interval Notation WS
1) Using the graph write:
-2
-1
0
1
2)
2
3
4
A) Write the set of all numbers less than 3
exclusive in interval notation?
A) As an inequality: _______________
B) Interval Notation: _______________
B) Express in interval notation: 6 < x
C) Set Builder Notation: _______________
3) A) Solve: x – 5 < -9.
4) A) Solve: 6x ≥ 18
B) Graph the solution on a number line.
B) Graph the solution on a number line.
Express the solution in:
Express the solution in:
C) Interval Notation: _______________
C) Interval Notation: _______________
D) Set Builder Notation: _______________
D) Set Builder Notation: ______________