Solving for \( x \): \( 6 + x = 0.05(300 + x) \) leads to \( 6 + x = 15 + 0.05x \).
["# Solving for ( x ): A Clear Step-by-Step Guide Using the Equation ( 6 + x = 0.05(300 + x) )", "When solving linear equations like ( 6 + x = 0.05(300 + x) ), it’s crucial to approach the problem methodically to arrive at the correct solution — and understand how simplifying leads to ( 6 + x = 15 + 0.05x ). This common algebra problem appears frequently in math education and real-world applications, making it essential to master the solution process.", "## Starting with the Equation", "Begin with the original equation:", "[\n6 + x = 0.05(300 + x)\n]", "Here, the left side represents a constant (6) plus the unknown ( x ), while the right side combines a constant (0.05 × 300 = 15) multiplied by ( (300 + x) ).", "## Distributing the 0.05", "Apply the distributive property to expand the right-hand side:", "[\n6 + x = 0.05 \ imes 300 + 0.05 \ imes x\n]", "[\n6 + x = 15 + 0.05x\n]", "This transformation confirms how the equation evolves, turning a balanced equation into a clearer form ready for further isolating ( x ).", "## Isolating ( x ) Terms and Constants", "Now, rearrange the equation to group like terms:", "[\n6 + x = 15 + 0.05x\n]", "Subtract ( 0.05x ) from both sides:", "[\n6 + x - 0.05x = 15\n]", "[\n6 + 0.95x = 15\n]", "Then subtract 6:", "[\n0.95x = 9\n]", "Finally, divide both sides by 0.95:", "[\nx = \frac{9}{0.95} = \frac{900}{95} = \frac{180}{19} \approx 9.47\n]", "## Why This Equation Matters", "This type of equation commonly arises in financial modeling (e.g., break-even analysis), physics (modeling linear relationships), and data interpolation. Solving for ( x ) reveals unknown quantities critical to decision-making. Understanding each step ensures accuracy and builds confidence in algebra.", "## Summary", "The equation ( 6 + x = 0.05(300 + x) ) simplifies cleanly to ( 6 + x = 15 + 0.05x ) through distribution and rearrangement — a routine yet powerful algebraic skill. With careful execution, you can confidently solve for ( x ) and apply these techniques across many practical scenarios.", "---", "Key SEO Keywords: solving linear equations, algebraic equations, intermediate algebra, distributive property, solving for ( x ), linear equation steps, equation simplification, math problem solving."]
