1. Warm Up Graph each set of numbers on a number line. -3, 7, -9
-2, -10, -8
3, -6, 10

2. Intro to Inequalities

3. Alex and Billy had a race!
Alex is faster than Billy!
FINISH
Alex
Billy

4. Do Alex and Billy have equal speeds?
Let a = Alex’s speed
and b = Billy’s speed
Does a = b?
No!
a > b

5. We call things like a > b inequalities because they are not equal.
Symbol
Words
Example Use
>
greater than
5 > 2
<
less than
7 < 9

6. Inequalities are easy to remember
Inequalities are easy to remember. The small end always points to the smaller number.
BIG
small
BIG
small

7. Example: Jacob plays under 15 soccer. How old is Jacob?
We don’t know how old Jacob is, but we know he is less than 15-years-old. Let j = Jacob’s age j < 15 The small end points to j because Jacob’s age is smaller than 15.

8. We can also have inequalities that include equals, like this:
Symbol
Words
Example Use ≥
greater than or equal to
x ≥ 1 ≤
less than or equal to
y ≤ 3

9. Example: You must be 13 years or older to watch a movie.
Let y be your age. You can be older than 13, but you can also be exactly 13. Since 13 is included, we use an inequality with an equals sign. y ≥ 13

10. How do we graph inequalities?
Step 1: Draw a number line. Step 2: Place a circle on the number in the inequality. Closed circle if the number is included, open circle if it is not. Step 3: Draw an arrow in the direction of the inequality.

11. Example: x < 2
Step 1: Draw a number line. Step 2: Place a circle on the number in the inequality. Closed circle if the number is included, open circle if it is not. Step 3: Draw an arrow in the direction of the inequality.

12. Example: x ≥ -3
Step 1: Draw a number line. Step 2: Place a circle on the number in the inequality. Closed circle if the number is included, open circle if it is not. Step 3: Draw an arrow in the direction of the inequality.

13. You try! Graph the following inequalities:
z < -2
4 > t
a ≥ -5
2 ≤ c