Simplify to \( 14x = 21 \), so \( x = \frac{21}{14} = \frac{3}{2} \).

["Simplify (14x = 21) to Find (x = \frac{3}{2}) – A Step-by-Step Guide", "Solving simple linear equations is a fundamental skill in algebra, and understanding how to simplify equations like (14x = 21) is essential for students and math learners. In this article, we’ll break down the process step by step to show how to solve (14x = 21) and arrive at the clean solution (x = \frac{3}{2}).", "---", "### Step 1: Understand the Equation", "We begin with the equation:", "[\n14x = 21\n]", "This equation states that 14 times some unknown value (x) equals 21. Our goal is to isolate (x) on one side of the equation.", "---", "### Step 2: Isolate the Variable (x)", "Because (x) is multiplied by 14, we use the reverse operation—division—to isolate (x). This means we divide both sides of the equation by 14:", "[\nx = \frac{21}{14}\n]", "Dividing both numerator and denominator by 7 simplifies the fraction:", "[\nx = \frac{3}{2}\n]", "This gives us the simplified exact value of (x).", "---", "### Step 3: Verify the Solution", "To ensure correctness, substitute (x = \frac{3}{2}) back into the original equation:", "[\n14x = 14 \left( \frac{3}{2} \right) = \frac{14 \cdot 3}{2} = \frac{42}{2} = 21\n]", "The left side equals the right side, confirming our solution is correct.", "---", "### Why This Method Works", "Simplifying equations by division is a direct application of the division property of equality, which states that dividing both sides of an equation by the same nonzero number preserves the equality. This technique keeps the solution clear and algebraically sound.", "---", "### Real-World Application", "Solving such equations helps solve everyday problems like proportional reasoning, budgeting calculations, and setting up ratios. It’s a building block for more advanced algebra and mathematical modeling.", "---", "### Summary", "To simplify (14x = 21) and find (x):", "1. Recognize (x) is multiplied by 14.\n2. Apply division: (x = \frac{21}{14}).\n3. Simplify: (x = \frac{3}{2}).\n4. Verify the solution by substitution.", "Mastering this process gives confidence in solving linear equations and develops strong foundational math skills.", "---", "Keywords: solve Eq (14x = 21), simplify algebra, isolate (x), divide both sides, rational solutions, mathematics tutorial, linear equations, (x = \frac{3}{2}), step-by-step algebra.", "---", "Mastering equations like (14x = 21) is simple—but essential for success in math. Keep practicing, verify your steps, and build your confidence!"]