Question:** The average of \( 2x+7 \), \( 5x-1 \), and \( 3x+4 \) is 24. What is the value of \( x \)?
["Title: How to Solve: The Average of (2x+7), (5x-1), and (3x+4) is 24 — Find the Value of (x)", "---", "Introduction\nStudents of algebra often encounter the concept of averages, especially when solving problems involving expressions. One common question is: “What is the average of (2x+7), (5x-1), and (3x+4) if it equals 24?” In this article, we’ll walk through step-by-step how to solve this type of problem, find the value of (x), and understand the logic behind calculating averages of linear expressions.", "---", "### What Does It Mean to Find the Average of Expressions?\nThe average of three numbers (or algebraic expressions) is simply their sum divided by three. When the problem gives an average and the expressions, your task is to:", "1. Express the average algebraically using the given terms.\n2. Set that average equal to the provided value (in this case, 24).\n3. Solve the resulting equation for (x).", "---", "### Step-by-Step Solution", "Step 1: Write the expression for the average\nThe three expressions are:\n[\n2x + 7, \quad 5x - 1, \quad 3x + 4\n]\nThe average is:\n[\n\frac{(2x + 7) + (5x - 1) + (3x + 4)}{3} = 24\n]", "Step 2: Combine like terms in the numerator\nAdd all the (x)-terms:\n[\n2x + 5x + 3x = 10x\n]\nAdd the constant terms:\n[\n7 - 1 + 4 = 10\n]\nSo the average becomes:\n[\n\frac{10x + 10}{3} = 24\n]", "Step 3: Eliminate the denominator by multiplying both sides by 3\n[\n10x + 10 = 24 \ imes 3\n]\n[\n10x + 10 = 72\n]", "Step 4: Solve for (x)\nSubtract 10 from both sides:\n[\n10x = 62\n]\nDivide by 10:\n[\nx = 6.2\n]", "---", "### Final Answer\nThe value of (x) that makes the average of (2x+7), (5x-1), and (3x+4) equal to 24 is:\n[\n\boxed{6.2}\n]", "---", "### Why This Method Works\nBy expressing the average algebraically and solving the resulting linear equation, we isolate (x) using standard algebraic rules. This approach applies to similar average problems involving any linear expressions, making it a foundational skill in algebra.", "---", "### Tips for Mastering Algebraic Averages\n- Always combine like terms before simplifying.\n- Multiply both sides by the denominator to eliminate fractions.\n- Double-check calculations by substituting (x = 6.2) back into the original expressions and verifying the average equals 24.\n- Practice with different variables and constants to build confidence.", "---", "### FAQ: Common Questions About Averages in Algebra\nQ: Can (x) be a fraction or decimal?\nA: Yes! Algebraic equations often have fractional or decimal solutions. Always simplify as much as possible.\nQ: What if the average isn’t a whole number?\nA: It’s still valid — use decimal or fractional forms.\nQ: How do I verify my answer?\nA: Plug (x = 6.2) back into each expression, add them, divide by 3, and confirm the result is 24.", "---", "Conclusion\nSolving for (x) when the average of algebraic expressions equals a number is a practical algebra skill. By combining terms, forming an equation, and isolating (x), you gain clarity in working with averages. Keep practicing — mastery comes with consistent application!", "---", "Keywords: average of algebraic expressions, solve for x algebraically, how to find x from average, solving linear equations with averages, average of (2x+7), (5x-1), (3x+4), algebraic problem-solving, step-by-step algebra guide, concreting algebra skills.", "---", "Meta Description:\nLearn how to find the value of (x) when the average of (2x+7), (5x-1), and (3x+4) equals 24. Step-by-step solving, algebraic explanations, and verification included. Perfect for algebra students."]
