9th Grade Algebra Notes
1. Expressions & Properties
● Variable: A symbol (usually a letter) that represents a number.
● Expression: A combination of variables, numbers, and operations.
● Order of Operations (PEMDAS):
1. Parentheses
2. Exponents
3. Multiplication/Division (left to right)
4. Addition/Subtraction (left to right)
Properties:
● Commutative: a + b = b + a, ab = ba
● Associative: (a + b) + c = a + (b + c)
● Distributive: a(b + c) = ab + ac
● Identity: a + 0 = a, a × 1 = a
● Inverse: a + (-a) = 0, a × (1/a) = 1
2. Solving Equations
● One-step equation: x + 5 = 12 → x = 12 - 5 → x = 7
● Two-step equation: 2x + 3 = 11 → 2x = 8 → x = 4
● Multi-step equations: Combine like terms, use distributive property if needed.
, 🎯 Goal: Isolate the variable.
3. Inequalities
● Symbols:
○ < less than
○ > greater than
○ ≤ less than or equal to
○ ≥ greater than or equal to
● Solve like equations, but:
○ Flip the inequality sign when multiplying/dividing by a negative number.
Example:
● −2x > 4 → x < −2 (flip sign)
4. Functions
● Function: A relation where each input has exactly one output.
● Written as: f(x) = expression
● Function notation:
If f(x) = 2x + 3, then f(2) = 2(2) + 3 = 7
● Linear Function: f(x) = mx + b
○ m = slope
○ b = y-intercept
1. Expressions & Properties
● Variable: A symbol (usually a letter) that represents a number.
● Expression: A combination of variables, numbers, and operations.
● Order of Operations (PEMDAS):
1. Parentheses
2. Exponents
3. Multiplication/Division (left to right)
4. Addition/Subtraction (left to right)
Properties:
● Commutative: a + b = b + a, ab = ba
● Associative: (a + b) + c = a + (b + c)
● Distributive: a(b + c) = ab + ac
● Identity: a + 0 = a, a × 1 = a
● Inverse: a + (-a) = 0, a × (1/a) = 1
2. Solving Equations
● One-step equation: x + 5 = 12 → x = 12 - 5 → x = 7
● Two-step equation: 2x + 3 = 11 → 2x = 8 → x = 4
● Multi-step equations: Combine like terms, use distributive property if needed.
, 🎯 Goal: Isolate the variable.
3. Inequalities
● Symbols:
○ < less than
○ > greater than
○ ≤ less than or equal to
○ ≥ greater than or equal to
● Solve like equations, but:
○ Flip the inequality sign when multiplying/dividing by a negative number.
Example:
● −2x > 4 → x < −2 (flip sign)
4. Functions
● Function: A relation where each input has exactly one output.
● Written as: f(x) = expression
● Function notation:
If f(x) = 2x + 3, then f(2) = 2(2) + 3 = 7
● Linear Function: f(x) = mx + b
○ m = slope
○ b = y-intercept
