Algebra Honors (period 4)

Solving Inequalities by Addition and Subtraction 5-1

An open sentence that contains < , >,   ≤, or  ≥  is an inequality.

Graphing an inequality
    Open dot  (○) is used for  <  or >
    Closed dot  (●) is used  for   ≤, or  ≥ 
(represents that it is either “ less than or EQUAL to”   or it is  “greater than or EQUAL to” )

Think of the = sign as a crayon that you can use to COLOR INT THE DOT
It is different from equations—Inequalities have many answers—in fact most of the time it is an infinite number of possibilities

n > 3 means that every real number greater than 3 is part of the solutions set  ( but NOT 3)
n ≥  3 still means that every real number greater than 3 is part of the solutions set, but now 3 is also a solution

Remember…graphing equation’s solution is easy! Let’s say you found that y = 5, you would just put a dot on 5 on the number line

Now with y ≥  5 you still put the dot on 5 but you also darken a line with an arrow going to the right to indicate all the numbers greater than 5 that are also solutions

With y > 5 you still have that line with an arrow going to the right of 5 but you use the OPEN DOT on 5 to indicate that 5 is NOT A SOLUTION

Translating words:
Some KEY words to know:

AT LEAST: means greater than or equal
NO LESS THAN : also means greater than or equal

I need at least $100 to go to the mall means I must have $100 but I would LOVE to have even more

AT MOST: means less than or equal
NO MORE THAN : also means less than or equal

I want at most 15 minutes of homework means that I will be okay with 15 minutes but I am hoping for even less!

Solving Inequalities with adding and subtracting

Use the additive Inverse Property as you would if you were balancing an equation. The only difference is that now you have more than one possible solution

5y + 4 > 29
You would subtract 4 from BOTH sides , then divide by 5 on each side

y > 5
Your answer is infinite because any real number bigger than 5 will work!

ALWAYS finish with the VARIABLE on the LEFT.

If you don’t, you may misunderstand the answer and graph it in the opposite position.
5 > y is NOT the same as y > 5

5> y means that y < 5

Check with whatever solution is easier in the solutions set—but NEVER USE the boundary number! It really does not help you see if your solutions are true!

Set builder notation

Get familiar with the following notation

{x│ x≥ 5} is read “ x SUCH THAT c is greater than or equal to 5”

Checking your solutions is an important set. Many students skip this step! Checking the solutions is especially important with inequalities because the direction of the inequality sign is often changed when writing solutions in set builder notation.