Divide both sides by 16: \( 26.25 = 2a + 12.4 \)

["# Solving the Equation: Divide Both Sides by 16 to Find ( a )", "When solving linear equations, one common step is simplifying expressions to isolate the variable. In this article, we’ll explore how to solve the equation\n[\n26.25 = 2a + 12.4\n]\nby carefully dividing both sides by 16 to find the value of ( a ), demonstrating clear mathematical reasoning and step-by-step explanation—perfect for students and learners seeking SEO-optimized guidance.", "---", "## Step-by-Step: Dividing Both Sides by 16", "Start with the original equation:\n[\n26.25 = 2a + 12.4\n]\nTo isolate the term with ( a ), first subtract 12.4 from both sides:\n[\n26.25 - 12.4 = 2a\n]\nCalculate the left-hand side:\n[\n13.85 = 2a\n]", "Now, to solve for ( a ), divide both sides by 2:\n[\na = \frac{13.85}{2} = 6.925\n]\nBut wait—what if we consider an alternate simplification approach involving dividing by 16?", "---", "## Understanding Why Dividing by 16 Matters", "Although the direct path uses subtraction and division by 2, sometimes equations are presented or manipulated using division by a common factor. Observing the original right-hand side—( 2a + 12.4 )—≤ note that 12.4 = ( \frac{16}{1.3} ) is not helpful directly. However, consider the simplified form:", "After isolating ( 2a ):\n[\n2a = 13.85\n]\nInstead of dividing 13.85 by 2 directly, suppose we wanted to divide everything—including the 2—by 16:\n[\n\frac{2a + 12.4}{16} = \frac{26.25}{16}\n]\nThis gives:\n[\n\frac{2a}{16} + \frac{12.4}{16} = \frac{26.25}{16}\n]\nSimplify each term:\n[\n\frac{a}{8} + 0.775 = 1.6421875\n]\nThen solve for ( a ):\n[\n\frac{a}{8} = 1.6421875 - 0.775 = 0.8671875\n\quad \Rightarrow \quad a = 8 \ imes 0.8671875 = 6.9375\n]\nWhile this method is valid, it’s more convoluted than direct simplification. For clarity and accuracy, dividing step-by-step by the smallest coefficient (2) remains the most efficient route.", "---", "## Final Answer: ( a = 6.925 )", "After performing the correct operations—subtract 12.4 from both sides, then divide by 2—we find:\n[\na = 6.925\n]", "Always verify your solution by plugging it back into the original equation:\n[\n2(6.925) + 12.4 = 13.85 + 12.4 = 26.25 \quad \ ext{✓}\n]", "---", "## Why This Equation Matters in Real Learning", "Solving equations by isolating variables strengthens algebra fundamentals. Understanding how coefficients and constants interact helps students tackle more complex problems in science, engineering, and finance. Mastering the order of operations—especially when dividing both sides—ensures precision and builds confidence in equation solving.", "---", "## SEO Keywords to Boost Visibility\n- Solve linear equation\n- Divide both sides by 16\n- Algebra step-by-step guide\n- Solve ( 2a + 12.4 = 26.25 )\n- How to isolate variable\n- Linear equation solving\n- Real-world algebra applications", "---", "## Conclusion", "Dividing both sides of ( 26.25 = 2a + 12.4 ) properly begins with subtraction and division by 2—not 16. Understanding when and how to simplify using direct coefficients keeps steps clear and accurate. Practice this process to master basic algebra and build a strong foundation for advanced math topics."]