Study Guide: Introduction to Algebra
Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities
in formulas and equations. It helps us solve problems where some values are unknown.
1. Variables
A variable is a letter (such as x or y) that represents an unknown value. For example: x + 5 = 12.
2. Expressions
An expression is a combination of numbers, variables, and operations. Example: 3x + 7.
3. Equations
An equation states that two expressions are equal. Example: 2x + 4 = 10. To solve it, isolate the
variable: 2x = 6 → x = 3.
4. Basic Algebra Rules
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Add or subtract the same value on both sides of an equation.
Multiply or divide both sides by the same number to isolate the variable.
Combine like terms (example: 2x + 3x = 5x).
5. Example Problems
Equation
Solution
x+4=9
x=5
2x = 14
x=7
3x + 3 = 12
x=3
x/2 = 6
x = 12
6. Practice Questions
1 Solve: x + 7 = 15
2 Solve: 4x = 20
3 Solve: 2x + 6 = 16