Solve: \( 1 + 4 = 4x - x \rightarrow 5 = 3x \rightarrow x = \frac{5}{3} \).

["# How to Solve ( 1 + 4 = 4x - x ): A Step-by-Step Guide", "Understanding how to solve simple algebraic equations is a crucial step in mastering math fundamentals. One common early algebra problem is solving ( 1 + 4 = 4x - x )—a straightforward equation that opens the door to understanding variables, simplification, and solving for unknowns like ( x ). In this article, we’ll break down the solution step-by-step, explain the logic behind each move, and show how this problem leads to the answer ( x = \frac{5}{3} ).", "---", "## The Equation: ( 1 + 4 = 4x - x )", "At first glance, the equation looks simple. But this expression tests key algebra concepts: combining like terms, simplifying expressions involving variables, and isolating the unknown variable. Let’s solve it comprehensively.", "---", "## Step 1: Simplify Both Sides", "Start with the base equation:", "[\n1 + 4 = 4x - x\n]", "- On the left side: ( 1 + 4 = 5 ), so now we have:\n [\n 5 = 4x - x\n ]", "- On the right side, combine like terms. Since both terms involve ( x ):\n [\n 4x - x = (4 - 1)x = 3x\n ]", "The equation simplifies to:\n[\n5 = 3x\n]", "---", "## Step 2: Isolate ( x )", "Now that both sides are simplified, you’re left with:\n[\n3x = 5\n]", "To solve for ( x ), divide both sides of the equation by 3:\n[\nx = \frac{5}{3}\n]", "---", "## Why This Works: Understanding the Solution", "This equation models a real-world scenario:\n- You started with a constant total of 5 (from 1 + 4).\n- You folded it down (subtracted ( x ) from ( 4x )), narrowing down to a value proportional to ( x ).\n- After simplifying ( 4x - x ) to ( 3x ), you turned the abstract into a solvable linear equation.", "Key algebraic skills demonstrated here include:\n- Combining like terms (simplifying ( 4x - x ))\n- Simplifying expressions involving variables\n- Isolating the variable using inverse operations", "---", "## Final Answer", "[\n\boxed{x = \frac{5}{3}}\n]", "---", "## Summary", "Solving ( 1 + 4 = 4x - x ) is more than just finding the number ( \frac{5}{3} )—it’s about building confidence in algebra by breaking problems down systematically. Practice this method with similar equations to strengthen your math foundation. Whether you’re a student, parent, or educator, mastering these steps unlocks deeper understanding of variables and equations.", "---", "### Additional Tips", "- Always simplify expressions before solving.\n- Understand what each step replaces to avoid mistakes.\n- Use fractions like ( \frac{5}{3} ) confidently—they’re standard in real-world applications.\n- Explore variations: What if the equation had subtraction instead of addition first? How do signs change the process?", "---", "Stay curious, practice daily, and watch your algebra skills grow!"]