Add/Subtract
x+10=30
x=20
Variable
A letter in an equation that represents an unknown number value
x, y, a, b
Fun fact: the letter 'o' is not generally used as a variable. Any guesses as to why?
1x = 3
x = 3
When solving an equation, how do you check to see if your answer is correct?
Plug it back into the original equation
Example:
x-4=9
x=13?
(13)-4=9
x-13=21
34
x รท 5 = 3
Operations
Addition, subtraction, multiplication, and division
Also: Parenthesis, exponents, factorials, logarithms
What operation is shown by the following? What is your answer?
3(2) =
Multiplication!
3(2) = 6
3 x 2 = 6
What is the overall goal of an equation with a variable in it?
To find the value of the variable (isolate the variable)
14 + x = 44
3x = 12
Inverse Operations
The opposite operation that undoes the original operation
Addition --- Subtraction
Multiplication ---- Division
How far away is the Sun from Earth?
93... MILLION miles away!
You could fit 12,000 Earths between here and the sun
What does an equal sign mean?
One side of the equation is the same value as the other side.
3=3
3=2+1
3+5 = 4+4
y=7
x * 8 = 72
x=9
Integer
A whole number (including negative numbers and zero)
Evaluate the following
32 =
9
3 x 3 = 9
How would you solve an equation with more than one operation attached to the variable?
Example:
4x + 3 = 11
Take it one step at a time!
Always undo addition/subtraction first, then multiplication/division second
Example:
4x + 3 = 11
-3 + 4 + x = 12
x/4 = 10
Reciprocal
The inverse operation of a fraction (a flipped fraction)
4/1 -> 1/4
What does PEMDAS mean?
Hint, the answer ISN'T "Please excuse my dear Aunt Sallie"
Parenthesis, Exponent, Multiply, Divide, Add, Subtract
Order of operations, the order in which you apply operations
What do you think you would do if you had a variable on BOTH sides of the equation?
Example: 2x = 3x + 1
Move all of the variables to ONE side of the equation
Example: 2x = 3x + 1
-3x -3x
-x = 1