Algebra Basics: Variables and Equations
Overview: Algebra is the language of mathematics that allows us to represent unknowns, relationships, and general rules. It can seem abstract at first, but once you see it as a tool for describing patterns, it becomes one of the most useful branches of math.
1. What is a variable?
A variable is a symbol (often a letter like x or y) that represents a number we don’t yet know. For example, if I say “I have x apples,” the letter x stands in place of the number of apples I have.
2. Expressions
An expression is a mathematical phrase that combines numbers, variables, and operations. For example: 3x + 5. This means “three times some number, plus five.” If x = 2, then the expression equals 11.
3. Simplifying expressions
We often want to make an expression as short and neat as possible. For instance:
2x + 4x - 3 simplifies to 6x - 3 because 2x + 4x = 6x.
4. Equations
An equation is like a balance scale: it shows that two sides are equal. Example: x + 3 = 7. Our goal is to find the value of x that makes the equation true. Here, x = 4.
5. Solving linear equations
Step-by-step process for solving 2x + 5 = 13:
- Subtract 5 from both sides →
2x = 8 - Divide both sides by 2 →
x = 4
6. Word problems
Algebra shines when applied to real situations. Example: “A movie ticket costs $8.50. You have $34. How many tickets can you buy?”
Equation: 8.5x = 34. Divide → x = 4. Answer: 4 tickets.
7. Common mistakes
- Forgetting to do the same operation to both sides of an equation.
- Mixing up variables with multiplication signs (write 2× instead of 2x).
- Not checking your answer by plugging it back into the equation.
Conclusion
Algebra is a skill that improves with practice. Begin by working with simple expressions and equations, and gradually take on more complex problems. With patience, the “mystery letters” become your best tool for problem solving.