Basic Concepts
In a nutshell: Expressions, equations, and inequalities are tools to represent and solve problems.
## Building and Solving
Mathematical expressions combine numbers, variables, and operations (like \( 3x + 2 \)). An equation is a statement that two expressions are equal, and an inequality shows one side is greater or less than the other.
### Solving Equations
To solve \( x + 5 = 12 \), subtract 5 from both sides to get \( x = 7 \). Balance is key!
### Graphing Inequalities
Use number lines to show solutions. For \( x > 3 \), shade all numbers to the right of 3.
### Applications
Equations and inequalities help with budgeting, planning events, and comparing options.
### Why Does It Matter?
Understanding equations helps you solve puzzles and real-world problems.
Examples
- If you have $20 and want to buy games that cost $x each, then \( 3x \leq 20 \) helps you decide how many you can buy.
- Solving \( 2y = 14 \) gives \( y = 7 \).