1. Inequalities
Objectives:
1. To identify symbols that represent inequalities
2. Write inequalities to represent situations
3. Graph inequalities on a number line
4. Use addition and subtraction to solve inequalities

2. ≤ Terminology: Inequality: A mathematical sentence that contains
_____, _____, _____, or _____ used to compare the values of two expressions.
Inequality symbols: ≤
>
<
>
- is less than
- is fewer than
- is greater than
- is more than
- exceeds
- is less than or
equal to
- is no more than
- is at most
Important!
The open side represents the __________ value
The closed side represents the _________ value.
Example:
When graphing inequalities, you use a ________________.

3. Write an inequality to represent each sentence:
1. Your age is greater than 14.
a. define your variable:
Let a = ______________
b. write your inequality:
_____________________
2. The restaurant can seat at most 172 people.
Let p = ___________________
___________________________

4. Translating verbal statements into mathematical/algebraic inequalities:
1. Two less than a number
2 < x
2. Four more than a number is greater than or equal to five
x + 4 > 5
3. The maximum value of a number is 28
x < 28
4. The sum of a number and nine is at least 81
x + 9 > 81
5. X is greater than or equal to 1
x > 1

5. Translating Practice:
1. The restaurant can seat no more than 164 people.
- select and define your variable
- write your inequality
2. At least 425 students can attend the concert.

6. Graph an inequality:
Steps:
1. Draw and label a ________________________
2. Place a closed circle ( for ____ or ____) or an open circle (for ____ or ____) on the value in the expression.
3. Draw a line with an ________, in the direction that represents the ____________ to the inequality.
Examples:
1. x < 8
2. x > -4

7. Practice:

8. Writing an inequality to represent a graph:
1. Determine what _______________________ to use based on the open or closed circle
2. Find the ____________ of the number the graph represents
3. Pick a ______________
4. Write your inequality

9. Write an expression that matches the graph of each inequality:1. 2. 3.

10. Solving inequalities using Addition/Subtraction:
Key: solving inequalties using addition and subtraction is just like equation solving with addition and subtraction.
Examples:
> x x - 15 < -6
3. d + 6 > a < 2.6

11. Practice:
1. v - 4 > > c + 31
> f < m

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