Solution: Compute $ f(3) = 9 - 18 + m = -9 + m $, and $ g(3) = 9 - 18 + 5m = -9 + 5m $. Set $ -9 + m = 2(-9 + 5m) $:

["Title: Solving the Equation: How to Compute and Solve $ -9 + m = 2(-9 + 5m) $", "When faced with a simple algebraic equation involving function values evaluated at the same point, the key is to carefully compute, substitute, and solve step by step. In this article, we’ll walk through solving the equation derived from transforming two functions: $ f(3) = 9 - 18 + m $ and $ g(3) = 9 - 18 + 5m $, setting $ f(3) $ equal to twice $ g(3) $. Let’s break down the solution clearly.", "---", "### Step 1: Compute $ f(3) $ and $ g(3) $", "Given:\n- $ f(3) = 9 - 18 + m = -9 + m $\n- $ g(3) = 9 - 18 + 5m = -9 + 5m $", "These expressions represent the values of two linear functions evaluated at $ x = 3 $. Substituting into their definitions gives a clear starting point.", "---", "### Step 2: Set up the Equation $ f(3) = 2 \cdot g(3) $", "According to the problem, we are told:", "$$\nf(3) = 2 \cdot g(3)\n$$", "Substitute the expressions:", "$$\n-9 + m = 2(-9 + 5m)\n$$", "---", "### Step 3: Expand the Right-Hand Side", "Multiply the right-hand side:", "$$\n-9 + m = 2 \cdot (-9) + 2 \cdot (5m) = -18 + 10m\n$$", "Now the equation becomes:", "$$\n-9 + m = -18 + 10m\n$$", "---", "### Step 4: Solve for $ m $", "Bring all terms involving $ m $ to one side and constants to the other:", "Subtract $ m $ from both sides:", "$$\n-9 = -18 + 9m\n$$", "Add 18 to both sides:", "$$\n9 = 9m\n$$", "Divide both sides by 9:", "$$\nm = 1\n$$", "---", "### Step 5: Verify the Solution", "Plug $ m = 1 $ back into the original expressions:", "- $ f(3) = -9 + 1 = -8 $\n- $ g(3) = -9 + 5(1) = -4 $\n- Check: Is $ -8 = 2 \cdot (-4) $? Yes, because $ 2 \ imes (-4) = -8 $", "The solution checks correctly.", "---", "### Why This Matters", "This type of problem showcases the power of substituting expressions from functions into algebraic equations. Whether in math competitions, online problem-solving, or real-world modeling, setting up accurate equations from function values and solving systematically is essential.", "---", "### Key Takeaways", "- Always simplify function expressions carefully.\n- Substitute values accurately into equations.\n- Use algebraic operations (like expanding, moving terms, dividing) to isolate variables.\n- Verify your solution by plugging it back in.", "---", "Final Answer: The solution is $ m = 1 $, satisfying the equation $ -9 + m = 2(-9 + 5m) $. Solve step-by-step: compute each function at $ x = 3 $, form the equality, expand, and simplify to isolate $ m $. Always check your result!", "---", "Keywords: solve algebra, function evaluation, linear equation, algebraic equation solution, step-by-step math tutorial, compute $ f(3) $, set up $ 2g(3) $, math practice, equation solving, verify solution, $-9 + m = 2(-9 + 5m)$", "---", "Effective function-based equations like this form a foundational skill in algebra. With consistent practice, solving equations derived from composed functions becomes intuitive and efficient."]