1. **Stating the problem:** We want to understand how to solve algebraic equations with examples. 2. **Formula and rules:** The main goal in algebra is to isolate the variable (usually $x$) on one side of the equation. We use operations like addition, subtraction, multiplication, and division, and apply the same operation to both sides to keep the equation balanced. 3. **Example 1:** Solve $2x + 3 = 7$ - Subtract 3 from both sides: $2x + 3 - 3 = 7 - 3$ - Simplify: $2x = 4$ - Divide both sides by 2: $\frac{2x}{2} = \frac{4}{2}$ - Simplify: $x = 2$ 4. **Example 2:** Solve $5x - 4 = 3x + 6$ - Subtract $3x$ from both sides: $5x - 3x - 4 = 3x - 3x + 6$ - Simplify: $2x - 4 = 6$ - Add 4 to both sides: $2x - 4 + 4 = 6 + 4$ - Simplify: $2x = 10$ - Divide both sides by 2: $x = 5$ 5. **Explanation:** In each step, we perform the same operation on both sides to keep the equation balanced. This helps us isolate $x$ and find its value. **Final answers:** - For example 1, $x = 2$ - For example 2, $x = 5$