Download 12-Inequalities with set and interval notation

CC Algebra I
CC Algebra I
Socci
12-Solving Inequalities
Number ______
Date: __________
Name: _________________________
Do Now:
1. Solve for x : 15 x  3(3x  4)  6
2. Which property is illustrated by the equation
6 + (4 + x) = 6 + (x + 4)
3. Which property of real numbers is illustrated
by the equation:
52 + (27 + 36) = (52 + 27) + 36
Key Concepts:
Set
Elements
The curly brackets indicate we are denoting a set.
Empty Set
Example:
Set Builder Notation:
a, b, c, d ,..... 
CC Algebra I
Example:
“The set of all integers that are greater than or equal to -3 and less than 100”
"The set of all real numbers that are not equal to zero"
*****The vertical bar " | " in this notation is often read as "that" or "such that"*****
When you solve an equation there will usually be only one answer in the set, but when
we solve inequalities there is more than once answer in the set
Symbol
Meaning
Less than
<
x3
Greater than
>
x 3
Less than or equal to
≤
x3
Greater than or equal to
≥
x3
Graphical Representation
CC Algebra I
Let’s explore some characteristics of inequalities!
Example 1
Solve 2x  3  7 , for x
Example 2:
What is the solution set to the inequality
5𝑞 + 10 > 20?
Express the solution set in words, in set notation,
and graphically on the number line.
Directions: Find the solution set to each inequality. Express the solution in set notation and
graphically on a number line
1. 6x  12  3x  6
2.  3(2 x  4)  0
3.
m
8  9
3
4.
8y  4  7 y  2
5.
 2k  16
6.
6( x  5)  30
CC Algebra I
Interval Notation
Interval notation is another way to represent a solution to an equation or an inequality, just as set
notation. In interval notation we use brackets and parentheses to represent solution sets.

[ ] means

( ) means

An infinity symbol will always use parentheses
Directions: Write the following graphical representations of solutions in interval notation
1.
2.
3.
4.
5.
6.
7.
8.
Directions: Find the solution set to each inequality. Express your answer in interval notation and
graphically on a number line
 3(2 x  4)  0
1. 4( x  3)  2( x  2)
2.
3.
.
5( x  3)  2 x  36
4.
x 1

12 4
1
x  3  2x  6
2
6.
 6x  7  8x  25
8.
21  5x  4x  6
5.
6.7. 12 x  4( x  5)
CC Algebra I
CC Algebra I
9. Sara has $53.50 in her pocket and wants to purchase shirts at a sale price of $14.95 each. AT MOST, how
many shirts can she buy?
10. The members of a school booster club are creating buttons for sale at basketball games. The machine to
make the buttons costs $45. The material need to make each button costs $0.20. The buttons will be sold for
$1 each. How many buttons must be sold to make a profit of at least $100.
11. At a amusement park, Kendra pays $15 to enter and $0.50 for each ride ticket. If she has $25,
what is the maximum number of ride tickets can she get?
12. Lisa brought half of her savings to the bakery and bought 12 croissants for $14.20. The amount of money
she brings home with her is more than $2.00. Use an inequality to find how much money she had in her
savings before going to the bakery. (Write the inequality that represents the situation, and solve it.)
CC Algebra I
Ms. Socci
Number ______
Date: __________________________
Lesson 20: Solving Inequalities
Do Now
1. Solve x -2 < -6
Graph:
0
2. Solve y + 4 > 7
Graph:
0
3. Solve 8y + 3 > 9y – 7
Graph:
0