1. Let's start by stating the problem: We want to understand what a linear equation is and how to work with it. 2. A linear equation in one variable is an equation that can be written in the form $$ax + b = 0$$ where $a$ and $b$ are constants and $a \neq 0$. 3. Important rules: - The variable $x$ is to the first power (no exponents other than 1). - The graph of a linear equation in two variables is a straight line. 4. To solve a linear equation, we isolate $x$ by performing inverse operations: 5. Example: Solve $$3x + 6 = 0$$ 6. Subtract 6 from both sides: $$3x + 6 - 6 = 0 - 6$$ $$3x = -6$$ 7. Divide both sides by 3: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{-6}{3}$$ $$x = -2$$ 8. So the solution to the linear equation $$3x + 6 = 0$$ is $$x = -2$$. 9. This means when $x = -2$, the equation holds true. 10. Linear equations are fundamental in algebra and appear in many real-world problems involving relationships with constant rates of change.