1. Let's create a similar algebra problem for practice. 2. Problem: Solve for $x$ in the equation $$3x - 7 = 2x + 5$$. 3. Formula and rules: To solve linear equations, we use the rule that we can add, subtract, multiply, or divide both sides of the equation by the same number without changing the equality. 4. Step 1: Subtract $2x$ from both sides to get all $x$ terms on one side: $$3x - 7 - 2x = 2x + 5 - 2x$$ $$\cancel{3x} - 7 - \cancel{2x} = \cancel{2x} + 5 - \cancel{2x}$$ $$x - 7 = 5$$ 5. Step 2: Add 7 to both sides to isolate $x$: $$x - 7 + 7 = 5 + 7$$ $$x = 12$$ 6. Final answer: $x = 12$ This problem is similar in structure and helps practice solving linear equations step-by-step.