Basic Concepts
In a nutshell: Use variables and expressions to represent and solve real-world problems.
## Algebra in Everyday Life
Algebra is like a math puzzle: you use letters to stand for numbers and then solve for them! This is super useful for figuring out unknowns.
### What’s an Expression?
An **expression** is a combination of numbers, variables, and operations (no equals sign). For example, \( 3x + 7 \).
### What’s an Equation?
An **equation** has an equals sign and shows that two things are the same. For example, \( 2y + 3 = 9 \).
### Tricks for Simplifying
- **Combine like terms:** \( 2x + 3x = 5x \)
- **Use properties:** Distributive property helps expand or factor expressions
### Why Learn This?
Algebraic thinking lets you describe real-life situations, like figuring out how many tickets you can buy with a set amount of money.
### Everyday Algebra
Planning a party with a budget? Let’s say the cost is \( 5x + 12 \). If each pizza costs $5 and decorations are $12, you can figure out how many pizzas you can afford.
Examples
- If \( x \) is the number of candies, and each costs $2, then \( 2x \) tells you the total price.
- Solving \( 3x + 4 = 10 \) tells you how many items you can buy with $10 if each costs $3 and there’s a $4 fee.
Key terms
- Variable
- A letter or symbol that stands for a number.
- Expression
- A combination of numbers, variables, and operations without an equals sign.
- Equation
- A statement that two expressions are equal.