1. Graphing & Writing Inequalities

2. What is an Inequality? > < > <
Inequality – a comparison of two expressions
>
– greater than
<
– less than
>
– greater than or equal to
<
– less than or equal to

3. Equation vs. Inequality?
Equation – uses an equal sign;
typically only one solution
Inequality – uses an inequality symbol;
infinite amount of solutions

4. Open Circle vs. Closed Dot
Hole (open circles) – are found when
there isn’t an “equal” involved in the sign
>
<
Dot (closed circles) – include that number that the dot in on (is an “equal” involved in sign)
>
<

5. Graphing Inequalities
Inequality
Word Sentence
Graph
x < 3
x is less than 3
Explanation: 3 is not included but all numbers less than 3 ARE included
x < 3
x is less than or equal to 3
Explanation: 3 IS included and all numbers less than 3 are also included

6. Graphing Inequalities
Inequality
Word Sentence
Graph
x > 3
x is greater than 3
Explanation: 3 is not included but all numbers greater than 3 ARE included
x > 3
x is greater than or equal to 3
Explanation: 3 IS included and all numbers greater than 3 are also included

7. Graphing Inequalities
Graph each inequality:
x > -2
4 > a

8. Graphing Inequalities
Graph each inequality:
y < -3
t < 0

9. Graphing Inequalities
Graph each inequality:
m > -4
t < 5

10. Writing Inequalities Word Sentence Inequality w > 6 x > 9
w is more than 6
x is at least 9
x > 9
k is at most -7
k < -7
g is less than 0
g < 0
8 is greater than j
8 > j

11. Adding & Subtracting Inequalities
We add and subtract inequalities just like equations – the inequality is like the equal sign
d < -2
d < 5

12. Adding & Subtracting Inequalities
We add and subtract inequalities just like equations – the inequality is like the equal sign
9 + a > 11
a > 2

13. Adding & Subtracting Inequalities
We add and subtract inequalities just like equations – the inequality is like the equal sign
1 + s < 5
s < 4

14. Adding & Subtracting Inequalities
We add and subtract inequalities just like equations – the inequality is like the equal sign
2 > n - 1
3 > n

15. Adding & Subtracting Inequalities
We add and subtract inequalities just like equations – the inequality is like the equal sign
3 + b < 1
b < -2

16. Solving Inequalities Multiplying & Dividing

17. Multiplying & Dividing Inequalities
We multiply and divide inequalities just like equations – the inequality is like the equal sign
One MAJOR exception:
When multiplying or dividing by a negative number, the inequality flips

18. Multiplying & Dividing Inequalities
Why does the inequality flip?
Example:
2 > -3
2 > -3
Multiply each side by a -1 for example
x x -1
-2 > 3
-2 is not greater than 3 so we have to flip the sign
-2 < 3

19. Multiplying & Dividing Inequalities
Why does the inequality flip?
Example:
8 > 6
8 > 6
Divide each side by a -2 for example
÷ ÷ -2
-4 > -3
-4 is not greater than -3 so we have to flip the sign
-4 <

20. Multiplying & Dividing Inequalities
Examples:
m > -5 14
m > -5 14
(14)
(14)
Multiply each side by 14
m > -70

21. Multiplying & Dividing Inequalities
Examples:
15n > 450
15n > 450
Divide each side by 15 15
n > 30

22. Multiplying & Dividing Inequalities
Examples:
-3a < 12
-3a < 12
Divide each side by -3 (notice we are dividing by a “negative” – sign will flip. -3 a
> -4

23. Multiplying & Dividing Inequalities
Examples:
x < 1 -2
x < 1 -2
(-2)
(-2)
Multiply each side by -2 – notice we are multiplying by a “negative” so the sign will flip x
> -2

24. Multiplying & Dividing Inequalities
Practice:
r < 3 -6
r > -18
-15s > 30
s < -2
8h > 32
h > 4
x < 10 2
x < 20

25. Inequalities Problem Solving
Chico is saving for new shoes that cost $87. He already has $9 saved, and he will save the same amount each week. Chico wants to but the shoes in 6 weeks. Use the inequality below to determine the least amount Chico can save each week and still buy the shoes in 6 weeks.
x ≥ 87
A.) $9
C.) $15
B.) $13
D.) $16