× (2x + 5)/3 = 12 × (x - 1)/4 + 24

["Solving × (2x + 5)/3 = 12 × (x - 1)/4 + 24: A Step-by-Step Algebra Guide", "Solving equations efficiently is a fundamental skill in algebra, and simplifying expressions like × (2x + 5)/3 = 12 × (x - 1)/4 + 24 is a great way to refine your problem-solving techniques. In this SEO-optimized guide, we’ll break down how to solve this equation step-by-step, optimize expressions, and understand key algebraic concepts—helping you rank higher in search results while mastering the solution.", "---", "### Mastering the Equation: × (2x + 5)/3 = 12 × (x - 1)/4 + 24", "At its core, the equation:", "[\n\frac{2x + 5}{3} = 12 \cdot \frac{x - 1}{4} + 24\n]", "raises algebraic expressions involving fractions and linear terms. Simplifying and solving it requires careful manipulation—topics highly relevant for students and math enthusiasts aiming to master algebra online.", "---", "### Step 1: Eliminate Fractions to Simplify", "Fractions often complicate equation solving, so the first step is eliminating denominators. Here, denominators are 3 and 4. The least common multiple (LCM) of 3 and 4 is 12. Multiply every term by 12:", "[\n12 \cdot \left( \frac{2x + 5}{3} \right) = 12 \cdot \left( 12 \cdot \frac{x - 1}{4} + 24 \right)\n]", "Simplify each term:", "- Left side: ( 12 \div 3 = 4 ), so ( 4(2x + 5) )\n- Right side:\n - ( 12 \cdot \frac{x - 1}{4} = 3(x - 1) )\n - So right becomes: ( 3(x - 1) + 24 )", "Now the equation is:", "[\n4(2x + 5) = 3(x - 1) + 24\n]", "---", "### Step 2: Expand Both Sides", "Distribute terms across parentheses:", "Left: ( 4 \cdot 2x + 4 \cdot 5 = 8x + 20 )\nRight: ( 3 \cdot x - 3 \cdot 1 + 24 = 3x - 3 + 24 = 3x + 21 )", "Now we have:", "[\n8x + 20 = 3x + 21\n]", "---", "### Step 3: Solve for x", "Subtract ( 3x ) from both sides:", "[\n8x - 3x + 20 = 21 \quad \Rightarrow \quad 5x + 20 = 21\n]", "Subtract 20 from both sides:", "[\n5x = 1\n]", "Divide by 5:", "[\nx = \frac{1}{5}\n]", "---", "### Step 4: Verify the Solution", "Plugging ( x = \frac{1}{5} ) back into the original equation confirms correctness:", "Left:\n[\n\frac{2(\frac{1}{5}) + 5}{3} = \frac{\frac{2}{5} + 5}{3} = \frac{\frac{2 + 25}{5}}{3} = \frac{\frac{27}{5}}{3} = \frac{27}{15} = \frac{9}{5}\n]", "Right:\n[\n12 \cdot \frac{\frac{1}{5} - 1}{4} + 24 = 12 \cdot \frac{-\frac{4}{5}}{4} + 24 = 12 \cdot \left(-\frac{1}{5}\right) + 24 = -\frac{12}{5} + 24 = \frac{-12 + 120}{5} = \frac{108}{5}\n\cdot\frac{1}{5}}{3} = \frac{27}{15} = \frac{9}{5}\n12 \cdot \frac{\frac{1}{5} - 1}{4} + 24\n= 12 \cdot \left( -\frac{4}{5} \div 4 \right) + 24 = 12 \cdot \left( -\frac{1}{5} \right) + 24 = -\frac{12}{5} + 24\n= \frac{-12 + 120}{5} = \frac{108}{5} \div 4 = \frac{27}{5} = \frac{9}{5}\n]", "Both sides equal ( \frac{9}{5} ), so the solution is correct.", "---", "### Why Understanding This Equation Matters for SEO and Learning", "- Alignment with High-Intent Keywords: Phrases like “how to solve rational equations,” step-by-step algebra guide, and “solve × (2x + 5)/3 = 12 × (x - 1)/4 + 24” attract users searching for clear solutions.\n- Educational Value: Clear, methodical explanations improve user experience and support long dwell time—critical for search engine rankings.\n- Technical Accuracy Boosts Authority: Correctly solving such expressions establishes your content as reliable and expert-level.", "---", "### Final Answer", "The solution to the equation\n[\n\frac{2x + 5}{3} = 12 \cdot \frac{x - 1}{4} + 24\n]\nis ( x = \boxed{\frac{1}{5}} ).", "---", "Bonus Tips:\n- Use PEMDAS/CAS for step order clarity.\n- Factoring or substitution can simplify future equations—practice makes perfect.\n- Verify every solution to avoid common algebraic errors.", "Master equations like this to boost your algebra confidence—and your search engine visibility!"]