Solve: \( 2x = 3 \), so \( x = rac{3}{2} \).

["# Solving Linear Equations: Understanding How to Find ( x ) in ( 2x = 3 )", "Learning how to solve linear equations is a foundational math skill that applies to many real-world scenarios, from simple financial calculations to complex scientific modeling. One of the most fundamental and commonly practiced problems is solving for ( x ) in a basic equation like ( 2x = 3 ). In this article, we’ll walk through how to solve this equation step-by-step and explain why the solution is ( x = \frac{3}{2} ).", "## What is the Equation ( 2x = 3 )?", "The equation ( 2x = 3 ) means that twice the value of ( x ) equals 3. We are tasked with finding the value of ( x ) that makes this statement true. Solving such an equation involves isolating the variable ( x ) by using inverse operations.", "## Step-by-Step Solution", "To solve ( 2x = 3 ), follow these clear mathematical steps:", "1. Identify the operation on ( x ):\n The variable ( x ) is multiplied by 2. To isolate ( x ), we apply the inverse operation—division.", "2. Divide both sides of the equation by 2:\n [\n 2x = 3 \quad \Rightarrow \quad \frac{2x}{2} = \frac{3}{2}\n ]", "3. Simplify:\n The left side simplifies to ( x ), since ( \frac{2x}{2} = x ). The right side remains ( \frac{3}{2} ).\n [\n x = \frac{3}{2}\n ]", "Thus, the solution is ( x = \frac{3}{2} ), which can also be expressed as the decimal ( 1.5 ).", "## Why Does ( x = \frac{3}{2} ) Work?", "You can verify the solution by substituting ( x = \frac{3}{2} ) back into the original equation:", "[\n2x = 2 \left( \frac{3}{2} \right) = 3\n]", "Since the left side equals the right side, our solution is correct.", "## Real-World Applications of Solving ( 2x = 3 )", "Understanding how to solve such equations helps in everyday problem-solving:\n- Budgeting: If twice your daily spending equals 3 dollars, you can determine how much you spend per day.\n- Physics: Determining unknown distances or times using proportional relationships often involves equations like this.\n- Education and standardized tests: Mastering linear equations is essential for success in algebra and advanced math courses.", "## Tips for Solving Similar Equations", "When you encounter equations of the form ( ax = b ), where ( a ) and ( b ) are known constants:\n1. Divide both sides by ( a ) to isolate ( x ).\n2. Always simplify fractions if possible.\n3. Check your solution by substituting it back into the original equation.", "## Conclusion", "Solving ( 2x = 3 ) to find ( x = \frac{3}{2} ) is a straightforward but powerful example of linear equation solving. Mastering this skill opens the door to more advanced algebra and practical problem-solving in everyday life. Keep practicing—you’re building a critical mathematical foundation!", "---", "Keywords: solve (2x = 3), linear equations, algebra, math tutorial, solve linear equations, value of (x), fraction to decimal, equation solving steps, real-world math applications."]