1. Stand Quietly

2. Lesson 4.1 Writing and Graphing Inequalities
Students will be able to write and graph inequalities

3. Warm-Up #37 1/4/17 Evaluate 5x + 6, given x=6
Evaluate 7m – 8, given m = 1 7
Evaluate 4 2 (𝑥−2), given x = -2

4. Homework 1/4/17
Textbook page 128 #6-9 #11-16

5. Homework Solutions

6. Homework 1/5/17
Worksheet: Lesson 4.1 Writing and Graphing Inequalities

7. Youtube

8. An inequality is like an equation, but instead of an equal sign (=) it has one of these signs:
< : less than
≤ : less than or equal to
> : greater than
≥ : greater than or equal to

9. greater than or equal to
<
>
less than
fewer than
greater than
more than
exceeds
less than or equal to
no more than
at most
greater than or equal to
no less than
at least
Inequality symbols

10. Example 1.
A number minus 4 is greater than 2. n - 4 > 2
The words "a number" tell us that we need a variable in our inequality, and that the result of the variable less "4" is more than 2.

11. Example 2.
The sum of x and 5 is less than or equal to -2.
x + 5 < -2
The words "the sum of" give us a clue that our inequality will involve addition.

12. Tell whether the given value is a solution of the inequality.
Example 1. 𝑛−7 <12;𝑛=6
𝟔−7 <12
−1 <12
True!

13. Tell whether the given value is a solution of the inequality.
Example 2. 2𝑛+1 ≥4;𝑛= 1 2
2( 𝟏 𝟐 )+1 ≥4
1+1 ≥4
2≥4
FALSE!

15. Exercise 2
Write an algebraic expression for each.
1) The greatest possible value of 3y is 30.  
2) The product of 3x and (3x + 1) is at least 35.
3) The minimum value of 2x + 1 is 13  
4) When x is divided by 3 the quotient is more than  
10 more than a number is greater than 50.
6) 10 more than the quotient of a number and 8 is at least 12.

16. Graphing Inequalities
When we graph an inequality on a number line we use open and closed circles to represent the number.
<
<
Plot an open circle ≤ ≥
Plot a closed circle

17. x < 5 means that whatever value x has, it must be less than 5.
Try to name ten numbers that are less than 5!

18. Numbers less than 5 are to the left of 5 on the number line.5 10 15
-20
-15
-10 -5
-25 20 25
If you said 4, 3, 2, 1, 0, -1, -2, -3, etc., you are right.
There are also numbers in between the integers, like 2.5, 1/2, -7.9, etc.
The number 5 would not be a correct answer, though, because 5 is not less than 5.

19. Try to name ten numbers that are greater than or equal to
x ≥ -2
means that whatever value x has, it must be greater than or equal to -2.
Try to name ten numbers that are greater than or equal to -2

20. Numbers greater than -2 are to the right of -2 on the number line.5 10 15
-20
-15
-10 -5
-25 20 25 -2
If you said -1, 0, 1, 2, 3, 4, 5, etc., you are right.
There are also numbers in between the integers, like -1/2, 0.2, 3.1, 5.5, etc.
The number -2 would also be a correct answer, because of the phrase, “or equal to”.