Definitions
Two terms with the same variable (or no variable).
What are like terms?
x = 5
Kevin is confused as to why there are numbers in math. These are called ____ and are used for ____.
What are 'variables' and 'to represent some unknown number'.
6x < 12
X < 2
Your friend trades you two and a half Cheetos, represented by the algebraic term (2c), for your sandwich. He then gives you one-third of his apple and a fruit cup free-of-charge. If you started with 18.75c Cheetos, how many do you have now?
18.75c - 2c = 16.75c
You now have 16 and three-quarters Cheetos, no sandwich, a mostly eaten apple, a fruit cup, and bad bargaining skills.
2x + 3
The '3' is called this.
What is a constant/numerical term?
3x - 12 = 12
x = 8
Kevin doesn't like to be a pessimist. So when he sees two negatives next to one another, he becomes distressed. Let's help Kevin. This is what we do for a problem like:
2 - (-4)
What is a double negative? Make the problem addition of a positive.
2 + 4x > 14
x > 3
A store sells x amount of tootsie roll pops (the good kind) for $0.25/piece. If they make $325, how many lollipops did they sell?
0.25x = 325
x = 325/0.25 = 1,300
They sold 1,300 lollipops, mostly to Mr. Malanga.
We use this for 'undoing' equations and inequalities.
What is an inverse operation?
3(2x) - 4.5 = -1.5
x = 1/2
Kevin says that it is a good idea to do this to PEMDAS when we solve equations or inequalities.
What is reverse the order of operations?
2(4.5 + 2x) > 25
x > 8
You go to get some sushi with friends. Your waiter is nice, so you decide to tip him 20%, because 18% is enough, but more difficult to calculate. If your bill is $40, how much did you tip your waiter?
$8
A law that allows you to move the order of addends around in any given expression.
What is the commutative property of addition?
2x - 3(4x + 2) = 5
x = -11/10
An international man/pumpkin of mystery.
Who is Kevin?
12x(-3) > 21
x < -7/12
You receive (12x + 32) watermelons as an inheritance from your Great Uncle Robert "Jiminy Cricket" Smith. You have to split the watermelons up amongst 4 people, yourself and your 3 brothers, Moe, Larry, and Curley. How much does each person receive?
4(3x + 8)
Each person gets (3x + 8) watermelons
A number that can be defined as m/n, where n is not '0' and 'm' and 'n' are both integers.
What is a rational number?
5.4(3a + 2.75) * 8 = 32
a = 0.638
Kevin's biggest pet peeve is when the signs (+/-) in his work get messed up. He doesn't remember what he could possibly do to keep this from happening. Other than 'don't get it wrong, Kevin', we could give him this other advice.
What is convert to addition of a negative?
2.25 + 4 1/3 < 3(2x - 4x) / -4.5
x > -4.935
Mr. Malanga is Christmas shopping, but doesn't want to spend too much, because he spent all of his last paycheck on tootsie roll lollipops (the good kind). He already bought a spiderman toy for his nephew for $7.50. If he doesn't want to spend more than $120 on gifts, how much could he spend (maximum) on his other 9 family members?
9x + 7.5 < 120
9x < 112.5
x < 112.5/9 = x < 12.5
Mr. Malanga can spend no more than $12.50 on each family member. Or, give everyone lollipops.