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Solving Equations with Fractions on Both Sides

🧮 Example: Solve: (2x/3) − (1/6) = (x/2) + (1/3) --- 🔍 Step 1: Identify the Denominators The denominators are: 3, 6, 2, and 3 To simplify, we eliminate the fractions by multiplying all terms by the Least Common Multiple (LCM) of these numbers. --- ✏️ Step 2: Find the LCM Let’s list a few multiples: Multiples of 2: 2, 4, 6, 8... Multiples of 3: 3, 6, 9... Multiples of 6: 6, 12, 18... ✅ The smallest common multiple is 6 So the LCM = 6 --- ✏️ Step 3: Multiply Every Term by 6 Now apply this to the equation: 6 × (2x/3) − 6 × (1/6) = 6 × (x/2) + 6 × (1/3) Now simplify: 6 × (2x/3) = 4x 6 × (1/6) = 1 6 × (x/2) = 3x 6 × (1/3) = 2 Now rewrite the new equation: 4x − 1 = 3x + 2 --- ✏️ Step 4: Solve the New Equation Now solve like a regular linear equation: 4x − 1 = 3x + 2 Subtract 3x from both sides: x − 1 = 2 Add 1 to both sides: x = 3 --- ✅ Final Answer: x = 3 --- 💡 Quick Tip: When dealing with equations that include fractions: Always begin by finding the LCM of all denominators. Multiply eve...
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Solving an Equation with Fractions

Solve: (1/2)x + (1/4) = 3/4 --- 🔍 Step 1: Understand the Problem This equation contains fractions, which makes it a bit harder to solve directly. To make it simpler, we will remove the fractions by using the LCM (Least Common Multiple) of the denominators. --- ✏️ Step 2: Find the LCM of the Denominators (2 and 4) Let’s list a few multiples: Multiples of 2: 2, 4, 6, 8, 10... Multiples of 4: 4, 8, 12... 👉 The LCM of 2 and 4 is 4 --- ✏️ Step 3: Multiply Every Term by the LCM Now multiply every term in the equation by 4 to remove the fractions: 4 × (1/2)x + 4 × (1/4) = 4 × (3/4) This simplifies to: 2x + 1 = 3 --- ✏️ Step 4: Solve the New Equation Now solve: 2x + 1 = 3 Subtract 1 from both sides: 2x = 2 Now divide both sides by 2: x = 1 ✅ Final Answer: x = 1 ---
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Solving Equations with Brackets on Both Sides

🧮 Example: Solve: 2(x + 3) = 3(x - 1) --- ✏️ Step 1: Expand Both Sides Use the distributive property: Left side: 2(x + 3) = 2x + 6 Right side: 3(x - 1) = 3x - 3 Now your equation becomes: 2x + 6 = 3x - 3 --- ✏️ Step 2: Move Variables to One Side Subtract 2x from both sides: 2x - 2x + 6 = 3x - 2x - 3   6 = x - 3 --- ✏️ Step 3: Solve for x Add 3 to both sides: 6 + 3 = x - 3 + 3   9 = x --- ✅ Final Answer: x = 9 --- 💡 Quick Tip: 👉 Always expand brackets first 👉 Move all variable terms to one side 👉 Move numbers to the opposite side 👉 Solve carefully, step by step! --- 🔗 Follow for More Lessons: 🌐 Website: www.easymathsguid.com.ng 📘 Blog: easymathsteps.blogspot.com ---
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