\[ 2x + 3(4x - 9) = 16 \]. - United Radiology

["# Solving the Linear Equation: 2x + 3(4x - 9) = 16", "Mastering how to solve linear equations is essential for students, math enthusiasts, and problem-solvers alike. At first glance, the equation 2x + 3(4x - 9) = 16 may seem tricky, but with a step-by-step approach, it becomes straightforward. In this SEO-optimized article, we’ll break down the solution process, explain each step clearly, and highlight the importance of simplifying expressions strategically. Whether you're preparing for algebra exams or simply improving your math skills, this guide will help you solve linear equations with confidence.", "## Understanding the Equation", "Before diving into solving, it’s important to understand the structure of the equation.
\n2x + 3(4x - 9) = 16 combines a variable term (2x) with a bracketed expression. The key to solving this equation lies in applying the distributive property correctly and combining like terms accurately.", "### Step 1: Apply the Distributive Property", "The expression involves multiplying 3 across the terms inside the parentheses:
\n3 × (4x - 9) = 3×4x - 3×9 = 12x - 27
\nRewriting the original equation:
\n2x + 12x - 27 = 16", "### Step 2: Combine Like Terms", "Now combine the x-terms on the left side:
\n2x + 12x = 14x
\nThe equation simplifies to:
\n14x - 27 = 16", "### Step 3: Isolate the Variable", "To solve for x, begin by adding 27 to both sides:
\n14x - 27 + 27 = 16 + 27
\nThis simplifies to:
\n14x = 43", "### Step 4: Solve for ( x )", "Divide both sides by 14:
\nx = 43 ÷ 14
\nx = 43/14", "This fraction is the precise solution, though it can also be expressed as a decimal: x ≈ 3.07, depending on your preferred form.", "## Why This Equation Matters", "Solving linear equations like 2x + 3(4x - 9) = 16 builds foundational algebra skills used in fields such as engineering, economics, and computer science. This particular equation demonstrates key concepts: distributing multipliers, combining like terms, and isolating variables—all crucial steps emphasized in standard algebra curricula.", "## Pro Tips for Solving Linear Equations", "- Always simplify parentheses first using the distributive property.
\n- Combine like terms early to simplify the workload.
\n- Isolate the variable step-by-step and perform the same operation on both sides to maintain equality.
\n- Check your solution by substituting back into the original equation.", "## Final Answer", "The solution to 2x + 3(4x - 9) = 16 is:
\nx = 43⁄14
\nor approximately x ≈ 3.07", "## Summary", "Solving 2x + 3(4x - 9) = 16 is a prime example of applying basic algebraic manipulation in a multi-step equation. By applying the distributive property, combining like terms, and isolating the variable, anyone can solve this equation efficiently. This type of problem-solving not only strengthens algebraic understanding but also prepares learners for more advanced math challenges.", "---
\nKeywords: linear equation, solve 2x + 3(4x - 9) = 16, algebraic equation, distributive property, solving for x, step-by-step math, algebra practice, equation-solving tips, math fundamentals."]