Solution: Multiply both sides by 6 to eliminate denominators: $ 4(x + 4) = 5(x - 1) $. Expand: $ 4x + 16 = 5x - 5 $. Rearrange: $ 16 + 5 = 5x - 4x \Rightarrow x = 21 $. The solution is $ \boxed{21} $.

["How to Solve Linear Equations: A Step-by-Step Guide Using Multiplication to Eliminate Denominators", "Solving linear equations is a fundamental skill in algebra, and one of the most effective strategies—especially when denominators are involved—is to multiply both sides of an equation by a common multiple, typically the denominator, to eliminate fractions and simplify calculations. This method streamlines the process and reduces the chance of errors. In this article, we’ll explore how multiplying both sides by 6 eliminates denominators in the equation:", "[\n4(x + 4) = 5(x - 1)\n]", "We’ll break down each step clearly to help students and lifelong learners master this essential technique.", "---", "### Step 1: Eliminate Denominators by Multiplying Both Sides by 6\nIn this equation, there are no denominators, but suppose the original equation had fractions—for example,\n[\n\frac{4}{6}(x + 4) = \frac{5}{5}(x - 1)\n]\nTo simplify and eliminate denominators, multiply every term by 6—the least common multiple (LCM) of 6 and 5. This removes the fractions swiftly:", "[\n6 \cdot \frac{4}{6}(x + 4) = 6 \cdot \frac{5}{5}(x - 1)\n]", "Simplifying, we get:\n[\n4(x + 4) = 5(x - 1)\n]", "This step transforms the equation into a cleaner, equivalent form ready for expansion.", "---", "### Step 2: Expand Both Sides\nNow expand each side using the distributive property (FOIL method):", "Left side:\n[\n4(x + 4) = 4x + 16\n]", "Right side:\n[\n5(x - 1) = 5x - 5\n]", "Putting it all together:\n[\n4x + 16 = 5x - 5\n]", "---", "### Step 3: Rearrange the Equation to Solve for ( x )\nNow, isolate variable terms on one side and constants on the other. Subtract ( 4x ) from both sides:", "[\n16 = 5x - 4x - 5\n]", "Simplify:\n[\n16 = x - 5\n]", "Add 5 to both sides:\n[\n16 + 5 = x \Rightarrow x = 21\n]", "---", "### Final Answer:\nThe solution to the equation is\n[\n\boxed{21}\n]", "---", "### Why This Method Works\nMultiplying both sides by a common denominator clears fractions, making the equation easier to manipulate algebraically. This technique is especially useful in word problems, real-world applications, and advanced math, where clean equations reduce computational errors and improve clarity.", "By consistently applying this step—multiply first to eliminate denominators, then expand, rearrange, and solve—you develop a reliable workflow for solving equations efficiently and accurately.", "Whether you're a high school student, college beginner, or someone brushing up on algebra, mastering this universal step lays a strong foundation for tackling more complex math challenges.", "---", "Key Takeaways:\n- Always clear fractions by multiplying both sides by the LCM of denominators.\n- Expand using distributive property.\n- Rearrange terms carefully to isolate ( x ).\n- Confirm your solution by substituting back into the original equation.", "Start practicing this method with simple equations—you’ll soon solve them with speed and confidence."]