Solving Equations
Solve for g:
4g = 12
g = 3
Function (rule): x2 - 6
Input (x): 0, 1, 5, 10, 14
Output (y): -6, -4, 4, 14, 22
What is a variable? How do we write a variable in algebra?
A variable is an unknown value / number. We usually use a letter to represent a variable (x, y, n, etc.)
Determine the pattern rule:
x y
1 6
2 12
3 18
4 24
5 30
Multiply by 6
Solve for p:
17 = p + 9
p = 8
Function (rule): /4 + 1
Input (x): 16, 8, 0, 40, 100
Output (y): 5, 3, 1, 11, 26
What is the difference between an expression and an equation. Give an example of each.
An equation has an equals sign (=). It has a left side and a right side. An expression does not have an equals sign.
Expression: 4x - 2 Equation: x + 5 = 21
Find the pattern rule:
x y
1 0
2 3
3 6
4 9
5 12
Multiply by 3, subtract 3
3x-3
Solve for e:
13 = 28 - e
e = 15
Function: y = x + 7
Input (x): 0, 1, 2, 3, 4
Output (y): 7, 8, 9, 10, 11
What does input pattern mean? Give an example.
How much the input changes by each time
Ex: start a 5, add 3 each time
Fine the pattern rule:
x y
1 9
2 11
3 13
4 15
5 17
Multiply by 2, add 7
2x+7
Solve for r:
5 + 4 + r = 12 - 2
r = 1
Function: y = 2x - 2
Input (x): 5, 2, 7, 10, 0
Output (y): 8, 2, 12, 18, -2
What does pattern rule stand for? Give an example.
How the input changes to the output
Find the pattern rule and the missing number:
x y
1 -7
2 -3
3 1
4 5
5 __
Multiply by 4, subtract 11
4x-11
Blank: 9
Solve for n:
6n - 11 = 7
n = 3
Function: y = x/2 - 6
Input (x): 6, 24, 100, 66, 15
Output (y): -3, 6, 44, 27, 1.5
Simplify the equation and then list the coefficient, constant, and variable in the following equation:
6x - 3 + x + 12 -2x = 43
5x + 9 = 43
constant= +9
Coefficient: 5
variable: x
Find the pattern rule and fill in the missing blank:
x y
1 -2
2 1
3 4
4 __
5 10
Multiply by 3, subtract 5
3x-5
Blank 2: 7