Basic algebra
What is Basic algebra?
A symbol, usually a letter, that represents a quantity that can change or is unknown.
Key formula / rule: Linear Equation in one variable
Key points
- Understand the concept of variables and constants.
- Formulate algebraic expressions from given information.
- Solve linear equations with one variable.
- Apply basic algebraic properties.
Common exam trap
Incorrectly applying the order of operations (PEMDAS/BODMAS).
Definitions
- Term
Variable
- Meaning
A symbol, usually a letter, that represents a quantity that can change or is unknown.
- Term
Constant
- Meaning
A fixed value that does not change.
- Term
Expression
- Meaning
A combination of numbers, variables, and mathematical operations that represents a value.
- Term
Equation
- Meaning
A mathematical statement that asserts the equality of two expressions, typically containing an equals sign (=).
- Term
Linear Equation
- Meaning
An equation in which each term is either a constant or the product of a constant and a single variable (raised to the power of 1).
Learning objectives
Understand the concept of variables and constants.
Formulate algebraic expressions from given information.
Solve linear equations with one variable.
Apply basic algebraic properties.
Interpret algebraic results in the context of a problem.
Formulae
- Name
Linear Equation in one variable
- Note
To solve for x, isolate it: x = (c - b) / a, provided a is not zero.
- Expression
ax + b = c
- Name
Distributive Property
- Note
Used to expand or factor expressions.
- Expression
a(b + c) = ab + ac
- Name
Commutative Property (Addition)
- Note
Order of operands does not change the result.
- Expression
a + b = b + a
- Name
Commutative Property (Multiplication)
- Note
Order of operands does not change the result.
- Expression
a * b = b * a
- Name
Associative Property (Addition)
- Note
Grouping of operands does not change the result.
- Expression
(a + b) + c = a + (b + c)
- Name
Associative Property (Multiplication)
- Note
Grouping of operands does not change the result.
- Expression
(a * b) * c = a * (b * c)
Prerequisites
Arithmetic operations (addition, subtraction, multiplication, division).
Understanding of numbers, including integers and fractions.
Basic concepts of equality.
Common mistakes
Incorrectly applying the order of operations (PEMDAS/BODMAS).
Errors in sign manipulation, especially with negative numbers.
Confusing expressions with equations.
Failing to perform the same operation on both sides of an equation.
Misinterpreting word problems into algebraic expressions.
Keywords
Algebra
Variable
Equation
Expression
Solve
Linear
Constant
Operation
Property
Practice preview
If 3x + 7 = 22, what is the value of x?…
easy
If x + y = 10 and x - y = 4, what are the values of x and y?…
medium
If a = 4 and b = 3, what is the value of 2a + 3b - 5?…
easy