\frac{10x + 10}{3} = 24

["How to Solve (\frac{10x + 10}{3} = 24): A Step-by-Step Guide", "Solving equations like (\frac{10x + 10}{3} = 24) is a fundamental skill in algebra that helps students, educators, and learners build strong problem-solving abilities. Whether you're a high school student, a college beginner, or someone revisiting basic math, knowing how to isolate (x) in this type of equation is essential. In this article, we’ll walk through the process clearly and provide practical tips to solve (\frac{10x + 10}{3} = 24) step-by-step.", "---", "### Understanding the Equation", "The equation\n[\n\frac{10x + 10}{3} = 24\n]\nrepresents a real-world situation where a linear expression (10x + 10) is divided by 3 and equals 24. Solving it helps determine the original value of (x) that satisfies this condition.", "---", "### Step-by-Step Solution", "Step 1: Eliminate the denominator\nTo simplify, multiply both sides of the equation by 3:\n[\n3 \cdot \left(\frac{10x + 10}{3}\right) = 3 \cdot 24\n]\n[\n10x + 10 = 72\n]", "---", "Step 2: Isolate the term with (x)\nSubtract 10 from both sides:\n[\n10x + 10 - 10 = 72 - 10\n]\n[\n10x = 62\n]", "---", "Step 3: Solve for (x)\nDivide both sides by 10:\n[\nx = \frac{62}{10} = 6.2\n]", "---", "### Verifying the Solution", "Plug (x = 6.2) back into the original equation:\n[\n\frac{10(6.2) + 10}{3} = \frac{62 + 10}{3} = \frac{72}{3} = 24\n]\nThe equation holds true, confirming the solution is correct.", "---", "### Practical Applications and Summary", "Solving equations like (\frac{10x + 10}{3} = 24) is not just academic—it applies to budgeting, physics, engineering, and everyday budgeting. For example, if (x) represents the number of hours worked at a rate involving fractions, this equation helps calculate income or break-even points.", "Final Answer:\n[\nx = 6.2\n]", "---", "### Summary Tips", "- Always eliminate denominators first for easier manipulation.\n- Perform inverse operations step-by-step to isolate (x).\n- Always verify your solution by substituting back into the original equation.", "---", "Keywords for SEO:\nfraction equation solving, solve (\frac{10x + 10}{3} = 24), algebraic equation step-by-step, linear equation solver, real-world math problems, algebra practice, how to solve equations", "---", "Start mastering your algebra today—understanding how to solve equations like (\frac{10x + 10}{3} = 24) opens doors to more complex mathematics and real-life problem-solving."]