Advanced Topics
In a nutshell: Inequalities and systems help you compare values and solve multi-step problems.
## Inequalities
Inequalities are like equations, but instead of an equal sign, they use \( <, >, \leq, \geq \) to show relationships.
- Example: \( x + 3 > 7 \) means any \( x \) greater than 4 is a solution.
## Systems of Equations
Sometimes, you need to solve more than one equation at the same time. This is called a system of equations.
- Example:
\[
\begin{align*}
x + y &= 10 \\
x - y &= 2
\end{align*}
\]
Solving this system helps you find the values of both \( x \) and \( y \).
## Applications
These topics are used in economics, science, and decision-making situations.
x > 4
Examples
- Solving \( 2x - 1 \leq 7 \) to find possible values for \( x \).
- Finding the price of two items when you know their total and their difference.
Key terms
- Inequality
- A mathematical sentence that shows the relationship between quantities that are not equal.
- System of Equations
- A set of equations with the same variables.