Algebra Honors ( periods 4 & 7)

Percent of Change 2-7

Percent of change is the ratio of the change over the original amount.

It can be an increase or a decrease.

Sometimes you know the percent of increase or decrease and you want to find either the original amount or the new amount.

Simply plug in the given information and solve for the missing item.

REAL LIFE APPLICATIONS OF PERCENTS OF CHANGE:

Percent of Decrease: Sales Tax or Discount

Sometimes a store will not tell you the percent off merchandise is…Instead, they’ll tell you the amount off.

You can find the discount % by looking at it as a percent of change.

Example:

A laptop is $100 off of the original price of $700. What is the discount percent?

The amount off is the change.

100/700 ≈ .143 or 14.3%

Percent of Increase: Markups

To make a profit, stores must mark up what they manufacture or buy to their customers.

That markup is an increase.

Example:

A company makes something that costs them $500 to produce. They mark it up $200 and sell it. What is their markup percent?

The $200 is the increase.

200/500 = .4 or 40% markup 

5-1 Solving Inequalities by Adding or Subtracting

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 answers (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

Graphing an equation's solution is easy
1) Say you found out 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

NO LESS THAN also means greater than or equal

AT MOST means less than or equal

NO MORE THAN also 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!

Solving Inequalities with adding and 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!

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 easiest in the solution set!

Set builder notation:

Get familiar with the following notation:

{x I x ≥ 5} which is read: “x SUCH THAT x is greater than or equal to 5.