\frac{(2x + 7) + (5x - 1) + (3x + 4)}{3} = 24

["Solving the Equation: (\frac{(2x + 7) + (5x - 1) + (3x + 4)}{3} = 24)", "When tackling algebraic equations, especially those involving fractions and multiple variables, clarity and step-by-step reasoning make all the difference. In this article, we’ll walk through the process of solving the equation:", "[\n\frac{(2x + 7) + (5x - 1) + (3x + 4)}{3} = 24\n]", "This type of problem often appears in middle school and high school math curricula and serves as a foundational exercise in solving rational equations and simplifying expressions. Let’s break it down.", "---", "### Step 1: Simplify the Numerator", "Before dividing by 3, combine like terms in the numerator:", "[\n(2x + 7) + (5x - 1) + (3x + 4)\n]", "Group the (x)-terms and constant terms separately:", "- (2x + 5x + 3x = 10x)\n- (7 - 1 + 4 = 10)", "So the expression simplifies to:", "[\n10x + 10\n]", "Now, rewrite the equation:", "[\n\frac{10x + 10}{3} = 24\n]", "---", "### Step 2: Eliminate the Denominator", "To eliminate the fraction, multiply both sides of the equation by 3:", "[\n10x + 10 = 3 \ imes 24\n]", "[\n10x + 10 = 72\n]", "---", "### Step 3: Isolate the Variable", "Subtract 10 from both sides:", "[\n10x = 72 - 10\n]", "[\n10x = 62\n]", "Now divide both sides by 10:", "[\nx = \frac{62}{10} = \frac{31}{5}\n]", "---", "### Final Answer", "[\n\boxed{x = \frac{31}{5}}\n]", "---", "### Why This Equation Matters", "Solving equations like this helps build critical algebraic skills such as combining like terms, simplifying expressions, and manipulating both linear and rational equations. These skills strengthen your ability to handle complex mathematical models in science, engineering, and economics.", "Try it yourself! Substitute (x = \frac{31}{5}) back into the original equation to verify your work. You’ll find the left side simplifies exactly to 24, confirming your solution is correct.", "Ready to level up your algebra? Practice similar problems daily—consistency is key to mastery!", "---", "Keywords for SEO:\nSolve linear equations, algebra practice, simplify rational equations, step-by-step equation solving, solve for (x), step-by-step math tutorial, elementary algebra problems, rational equation examples, middle school math, high school algebra homework help"]