Name: ________________________________
Unit 4: Solving Inequalities
Integrated Algebra 1A
Day 2: Inequality Notation
Homework: Day 2 Homework Worksheet (Inequality Notation)
Set Builder Notation vs. Interval Notation
Set Builder
Notation
{x|x is a real number,
1 < x < 5}
{x|x is a real number,
1  x  5}
{x|x is a real number,
1 < x  5}
{x|x is a real number,
1  x < 5}
{x|x is a real number,
x > 1}
{x|x is a real number,
x  5}
Sometimes the solution set does not include all the real numbers. When this happens, just use dots on
the number line or if in set-builder, write a sentence describing the types of numbers (i.e. integers,
natural numbers, evens, odds, etc).
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Let’s rewrite each set of numbers in set-builder notation.
•
•
Roster form lists the elements of a set within braces, { }.
Set-builder notation describes the properties an element must have to be included in a set.
How do you write “R is the set of even whole numbers less than 10” in roster form, set-builder
notation and on a number line?
Roster Form
List the numbers 0, 2, 4, 6, and 8 in braces.
R = {0, 2, 4, 6, 8}
Set-Builder Notation
Describe the properties.
R = {x | x is an even whole number, x < 10}
This is read as “R is the set of all numbers x such that x is an even whole number less than 10.”
Number Line
Write each set in roster form and in set-builder notation.
1.
D is the set of integers greater than –5 and less than 5.
2.
N is the set of odd integers less than 14.
3.
P is the set of integers greater than or equal to 7.
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4.
T is the set of natural numbers that are factors of 18.
5.
A is the set of integers between –3 and 5, inclusive.
6.
B is an odd integer.
Solve the inequality. Then 1) graph the solution on a number line 2) write the solution in interval
notation 3) write the solution in set-builder notation. Notice, your answers include decimals and
fractions so your set of numbers is all real numbers!
1. 4b + 8 > –12
2. 7n – 14 ≥ 28
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3. 5s – 15 ≤ 18 – 2s
4. 2(3p – 5) – 7p < –2
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