Solution: Solve $ x = 3 - rac{1}{2} = rac{5}{2} $. Substitute into $ 4x + 2 $: $ 4 imes rac{5}{2} + 2 = 10 + 2 = 12 $.
["### Solving Simple Equations: How to Solve $ x = 3 - \frac{1}{2} = \frac{5}{2} $ and Substitute into $ 4x + 2 $", "Learning how to solve equations is a fundamental skill in mathematics—essential for students, educators, and lifelong learners alike. Today, we explore a clear and practical example: solving for $ x $ in the equation $ x = 3 - \frac{1}{2} $, simplifying step by step, and substituting that value into a larger expression like $ 4x + 2 $. This process not only reinforces basic algebra but also demonstrates real-world problem-solving techniques.", "---", "#### Step 1: Solve $ x = 3 - \frac{1}{2} $", "To find $ x $, evaluate the expression on the right-hand side:", "$$\nx = 3 - \frac{1}{2}\n$$", "Convert 3 to a fraction with denominator 2:", "$$\n3 = \frac{6}{2}\n$$", "Now subtract:", "$$\nx = \frac{6}{2} - \frac{1}{2} = \frac{5}{2}\n$$", "So,", "$$\nx = \frac{5}{2}\n$$", "---", "#### Step 2: Substitute $ x = \frac{5}{2} $ into $ 4x + 2 $", "Next, substitute $ x = \frac{5}{2} $ into the expression $ 4x + 2 $:", "$$\n4x + 2 = 4 \left( \frac{5}{2} \right) + 2\n$$", "Multiply:", "$$\n4 \ imes \frac{5}{2} = \frac{20}{2} = 10\n$$", "Add 2:", "$$\n10 + 2 = 12\n$$", "Therefore,", "$$\n4x + 2 = 12\n$$", "---", "#### Why This Pattern Matters", "This basic algebraic substitution—solving for $ x $, simplifying expressions, then plugging values back in—is the foundation for solving more complex equations and real-world mathematical modeling. Whether you're calculating costs, analyzing trends, or designing algorithms, understanding how to manipulate and substitute values ensures accuracy and clarity.", "---", "#### Final Answer", "$$\nx = 3 - \frac{1}{2} = \frac{5}{2} \\n4x + 2 = 4 \ imes \frac{5}{2} + 2 = 10 + 2 = \boxed{12}\n$$", "---", "Keywords for SEO: solve linear equations, algebra tutorial, substitute variables, simplify expressions, $ 4x + 2 example, solve $ x = 3 - \frac{1}{2} $, step-by-step math, real-world math problem, fraction arithmetic, evaluate algebraic expressions."]
