4(2x - 1) = 5(x + 3)

["Solving 4(2x - 1) = 5(x + 3): A Step-by-Step Guide", "Mastering algebra is essential for students and learners of all levels, and one of the core skills is solving linear equations—like 4(2x - 1) = 5(x + 3). Whether you're preparing for a test, strengthening math fundamentals, or teaching someone else, this article breaks down the solution clearly and provides useful tips to solve similar equations in the future.", "---", "### Understanding the Equation", "The equation 4(2x - 1) = 5(x + 3) is a typical linear equation involving parentheses and variables on both sides. Before jumping into solving, it’s important to simplify both sides using the distributive property (also known as expanding).", "---", "### Step-by-Step Solution", "Step 1: Expand both sides", "Start by applying the distributive property:", "- Left side:\n (4 \ imes 2x - 4 \ imes 1 = 8x - 4)", "- Right side:\n (5 \ imes x + 5 \ imes 3 = 5x + 15)", "Now the equation becomes:\n[\n8x - 4 = 5x + 15\n]", "---", "Step 2: Get all variable terms on one side", "Subtract (5x) from both sides to collect (x) terms on the left:\n[\n8x - 5x - 4 = 15\n]\n[\n3x - 4 = 15\n]", "---", "Step 3: Isolate the variable term", "Add 4 to both sides:\n[\n3x = 19\n]", "---", "Step 4: Solve for (x)", "Divide both sides by 3:\n[\nx = \frac{19}{3}\n]", "---", "### Final Answer", "[\n\boxed{x = \frac{19}{3}}\n]", "---", "### Why This Equation Matters", "- It demonstrates the use of distributive property to eliminate parentheses.\n- It reinforces combining like terms and isolating variables—key algebraic techniques.\n- It helps build problem-solving confidence for more complex equations.", "---", "### Tips for Quickly Solving Similar Equations", "1. Always expand parentheses first.\n2. Group like terms on each side.\n3. Move variables to one side and constants to the other using addition/subtraction.\n4. Use inverse operations (addition/subtraction, multiplication/division) to solve.\n5. Check your solution by plugging (x = \frac{19}{3}) back into the original equation.", "---", "### Practice Problems", "Try solving these similar equations to master the technique:\n- (3(2x + 4) = 2(x - 5))\n- (5(x - 2) + 3 = 4(2x + 1))\n- (7(3x + 1) = 2(5 - x))", "---", "### Conclusion", "Solving 4(2x - 1) = 5(x + 3) is a straightforward process using distributive expansion and basic algebra. By following step-by-step simplification and isolating (x), anyone can arrive at the correct solution efficiently. Consistent practice turns algebra into a powerful tool—not a daunting challenge.", "---", "Keywords:\n4(2x - 1) = 5(x + 3), solve linear equation, algebra tutorial, distributive property, solving for x, step-by-step equation solving, algebra practice problems, fundamental algebra skills, math homework help, equations with parentheses."]