Rearranging gives \( x - 0.05x = 15 - 6 \), so \( 0.95x = 9 \).

["# Rearranging the Equation: Understanding ( 0.95x = 9 )", "Solving linear equations is a fundamental skill in algebra, crucial not only for math students but also for anyone interested in quantitative reasoning—from finance to engineering. One important equation you might encounter is:", "[ x - 0.05x = 15 - 6 ]", "At first glance, rearranging this expression may seem straightforward, but understanding how to manipulate and simplify it reveals key algebraic strategies. In this article, we’ll explore the step-by-step process of rearranging the given equation into the equivalent form ( 0.95x = 9 ), highlight the role of coefficient simplification, and explain the practical value of mastering such manipulations.", "---", "### Step-by-Step: Rearranging ( x - 0.05x = 15 - 6 )", "The original equation is:\n[ x - 0.05x = 15 - 6 ]", "#### Step 1: Simplify Both Sides", "Start by reducing both sides of the equation as much as possible.", "- Left side: ( x - 0.05x = (1 - 0.05)x = 0.95x )\n- Right side: ( 15 - 6 = 9 )", "So the equation becomes:\n[ 0.95x = 9 ]", "---", "### Why This Works: The Algebra Behind It", "To fully understand the rearrangement, let’s break down the algebraic principle at work.", "Starting from:\n[ x - 0.05x = 15 - 6 ]", "We recognize both terms on the left represent like terms: coefficients of ( x ). Combining them gives:\n[ (1 - 0.05)x = 9 \Rightarrow 0.95x = 9 ]", "This simplification relies on the distributive and combining like terms rules—cornerstones of algebraic manipulation.", "---", "### Solving for ( x ): A Quick Follow-Up", "While not directly asked, solving fully gives:\n[ x = \frac{9}{0.95} = \frac{900}{95} = \frac{180}{19} \approx 9.47 ]", "But even without the decimal, expressing ( 0.95x = 9 ) simplifies future computations.", "---", "### Practical Applications of Rearranging Linear Equations", "Understanding how to rearrange equations like ( x - 0.05x = 15 - 6 ) is critical in real-world scenarios:", "- Finance: Modeling fees or discounts applied over multiple periods.\n- Science: Calculating rate changes or proportional variations.\n- Everyday problem-solving: Interpreting relative changes such as percent decreases.", "When you reduce an equation to the form ( Cx = D ), solving for ( x ) becomes simple and error-resistant—especially valuable in data analysis or programming.", "---", "### Tips to Master Equation Rearranging", "- Group like terms first: Combine coefficients and constants to simplify expressions before solving.\n- Use inverse operations: To isolate ( x ), subtract if needed, then divide by the coefficient.\n- Verify solutions: Plug values back into the original equation to ensure accuracy.\n- Embrace fractions: Convert decimals to fractions (like ( 0.05 = \frac{1}{20} )) to avoid rounding errors in exact calculations.", "---", "### Final Thoughts", "Mastering the rearrangement of equations such as ( x - 0.05x = 15 - 6 ) to ( 0.95x = 9 ) goes beyond algebra—it’s a gateway to clearer thinking and problem-solving prowess. By combining like terms efficiently and applying basic algebra, anyone can build confidence in tackling equations that model real-life situations.", "If you're learning algebra or looking to sharpen your math skills, practicing equation manipulation remains one of the most rewarding and practical investments.", "---", "### Key SEO Keywords\n- Rearranging linear equations\n- How to simplify ( x - 0.05x = 15 - 6 )\n- Step-by-step algebra solution\n- Solve ( 0.95x = 9 )\n- Algebraic simplification for beginners\n- Real-world math applications", "Optimize your learning with clear explanations, practical examples, and step-by-step guidance—because mastering equations starts with mastering the rearrangement."]