1. Inequalities Today’s Lesson: What: Why:
so I can identify and graph inequalities.

2. How are equations
and inequalities
different?

3. Why is it important to re-write inequalities with “x” on the left of the inequality sign?

4. What is an inequality?? balanced
An inequality is a math sentence that describes two or more quantities
that are _______ equal.
In other words, the left and right sides of the inequality are NOT __________________ .
NOT
balanced

5. inequality symbols . . .

6. What does an inequality have to do with real life??
Real-life examples . . .
What does an inequality have to do with real life??
Consider the following sign:
If x represents speed . . .
Inequality for obeying the speed limit:
Inequality for not obeying the speed limit:
x ≤ 55
x > 55

7. Real-life examples . . . 48” x ≥ 48 x < 48
Consider the following sign:
BE AT LEAST THIS TALL
If x represents height . . .
Inequality for being able to ride:
Inequality for not being able to ride:
x ≥ 48
x < 48

8. Real-life examples . . . x ≤ 10 x > 10 Consider the following sign:
If x represents age . . .
5) Inequality for eating free:
6) Inequality for not eating free:
x ≤ 10
x > 10

9. x is ALL numbers SMALLER x is ALL numbers BIGGER OR EQUAL to 12.
What does it mean??
In an equation, the variable (x) represents ONE number.
Is this true in an inequality??
Consider the following inequalities . . .
1) x > Meaning:
2) x ≤ Meaning:
x is ALL numbers SMALLER
OR EQUAL to 6.
x is ALL numbers
BIGGER than 25.
3) x < Meaning:
4) x ≥ Meaning:
x is ALL numbers BIGGER OR EQUAL to 12.
x is ALL numbers
SMALLER than 10.

10. for the test. . .
Circle EVERY number that could be a solution to the following inequalities :
x ≥ -6 -6
-6.5 -7 6
x < -3
-3.5 -5 -3 -2

11. How can you remember that? Here’s a little trick:
graphing an inequality. . .
Open or Closed Circle??
When graphing the answer to an inequality on a number line, we
use an __________________ circle for > or < signs, and a ________________ circle for ≥ or ≤ signs.
How can you remember that? Here’s a little trick:
DOES THE BIRD GET THE WORM ?!?
If the bird “gets the worm,” his belly is full,
So we use a _______________________ circle.
If the bird does NOT get the worm, his belly
Is empty, so we use an _______________ circle.
open
closed
closed ( )
open ( )

12. Graph the following inequalities on the given number lines:
x ≥ -4
2) x < -4

13. x > -1
x ≤ 2
What about when “x” is on the right side of the inequality??
Consider the following: > x
Use common sense:
If 4 is greater than x, then x must be LESS than 4 !
If your age is greater than your sister’s age,
then your sister’s age must be _________ than your age!
Makes sense.
x < 4
less

14. What about when “x” is on the right side
of the inequality??
In order to reduce careless mistakes, we should re-write the inequality,
placing “x” on the LEFT side. HOWEVER, remember to also switch the sign!!
Let’s practice . . .
Graph the following inequalities on the given number lines (re-write first):
5 ≥ x
x ≤ 5
x ≤ 5
0 < x
x > 0
7 > x
x < 7
We want “x” on the LEFT!!

15. Wrap it up/Summary: How are equations and inequalities different?
Why is it helpful to re-write inequalities with the “x” on the left of the inequality sign?
Equations:
Balanced
There is only 1 answer
Inequalities:
Not balanced
There are many answers
Because our brains think “left-to-right,” it helps to understand the meaning of the inequality.
It makes it easier to graph 

16. video challenge. . .

17. END OF LESSON