Algebra Period 4

Inequalities & Their Graphs 4-1
Introduction to INEQUALITIES and graphing them:

Writing an inequality

Graphing an inequality - open dot is < or >

Closed dot mean less than or EQUAL or greater than or EQUAL
(think of the = sign as a crayon that you can use to COLOR IN THE DOT!)

Different from equations: Inequalities have many solutions (most of the time an infinite number!)

Example: n > 3 means that every real number greater than 3 is a solution! (but NOT 3)

n ≥ 3 means still means that every real number greater than 3 is a solution, but now 3 is also a solution.
The endpoint ( in this case 3) is called the boundary point.


GRAPHING INEQUALITIES:

First, graphing an equation's solution is easy

1) Let's say you solved an inequality and you discovered that y = 5, you would just put a dot on 5 on the number line

2) But now you have the y ≥ 5

You still put the dot but now also darken in an arrow going to the right

showing all those numbers are also solutions

3) Finally, you find in another example that y > 5

You still have the arrow pointing right, but now you OPEN THE DOT on the 5 to show that 5 IS NOT A SOLUTION!


TRANSLATING WORDS:

Some key words to know
AT LEAST means greater than or equal

AT MOST means less than or equal


I need at least $20 to go to the mall means I must have $20, but I'd like to have even more!

I want at most 15 minutes of homework means that I can have 15 minutes,
but I'm hoping for even less!



The Addition Property of Inequalities 4-2

Solving Inequalities with adding or subtracting

Simply use the Additive Inverse Property as if you were balancing an equation!

The only difference is that now you have more than one possible answer.

Example: 5y + 4 > 29

You would -4 from each side, then divide by 5 on each side and get:
y > 5

Your answer is infinite! Any real number bigger than 5 will work!
It is IMPOSSIBLE to check every value in an infinite solution set. However, once you have determined the endpoint-- or boundary point, you can verify by checking a representative or sample number from the supposed solution set to verify that your inequality has been solved correctly.