1. Let's start by stating the problem: We want to understand how to solve algebraic equations using examples. 2. The general formula or approach for solving linear equations is to isolate the variable on one side of the equation. For example, for an equation $ax + b = c$, we solve for $x$ by subtracting $b$ from both sides and then dividing by $a$: $$x = \frac{c - b}{a}$$ 3. Important rules to remember: - You can perform the same operation on both sides of the equation. - Addition and subtraction undo each other. - Multiplication and division undo each other. 4. Example 1: Solve $2x + 3 = 7$ - Subtract 3 from both sides: $2x + 3 - 3 = 7 - 3$ which simplifies to $2x = 4$ - Divide both sides by 2: $x = \frac{4}{2} = 2$ 5. Example 2: Solve $5x - 10 = 0$ - Add 10 to both sides: $5x - 10 + 10 = 0 + 10$ which simplifies to $5x = 10$ - Divide both sides by 5: $x = \frac{10}{5} = 2$ 6. Example 3: Solve $3(x - 2) = 9$ - First, divide both sides by 3: $x - 2 = \frac{9}{3} = 3$ - Then add 2 to both sides: $x = 3 + 2 = 5$ These examples show how to isolate the variable step-by-step to find the solution. Final answers: - Example 1: $x = 2$ - Example 2: $x = 2$ - Example 3: $x = 5$