Easymathsteps

Now that we've solved equations with fractions, let’s learn how to solve equations where you need to multiply fractions to get the variable. --- ✏️ Concept: To solve equations like: (fraction) × x = value You need to multiply both sides of the equation by the reciprocal of the fraction to isolate x. > ✨ The reciprocal of a fraction is when you flip the numerator and denominator. --- 📘 Example 1: Solve: (2/3) × x = 6 To eliminate the fraction, multiply both sides by the reciprocal of 2/3, which is 3/2: x = 6 × (3/2) x = 18/2 = 9 ✅ Final Answer: x = 9 --- 📘 Example 2: Solve: (5/8) × x = 10 Multiply both sides by 8/5: x = 10 × (8/5) x = 80/5 = 16 ✅ Final Answer: x = 16 --- 📝 Practice Questions: 1. (3/4) × x = 9 2. (7/2) × x = 14 3. (4/5) × x = 20 4. (2/3) × x = 10 5. (9/10) × x = 18 --- ✅ Answers: 1. x = 12 2. x = 4 3. x = 25 4. x = 15 5. x = 20 --- 📘 Want more lessons? Visit us: 🔗 Blog: https://easymathsteps.blogspot.com 🌐 Website:https://www.easymathsguid.com.ng 

🧮 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...

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 ---

🧮 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 ---

🧮 Example: Solve: 2(x + 3) = 14 --- ✏️ Step 1: Expand the Bracket Use the distributive property: Multiply 2 by x and 3: 2 × x = 2x   2 × 3 = 6 So the equation becomes: 2x + 6 = 14 --- ✏️ Step 2: Solve the Equation Now subtract 6 from both sides: 2x = 14 - 6   2x = 8 Divide both sides by 2: x = 8 ÷ 2   x = 4 --- ✅ Final Answer: x = 4 --- 💡 Quick Tip: Always expand the brackets first before solving the equation. Then follow the steps you've already learned: move constants, isolate the variable, and solve. --- 🔗 Follow Easymathsguid for More Lessons: 🌐 Website: www.easymathsguid.com.ng 📘 Blog: easymathsteps.blogspot.com

🧮 Example: Solve: 3x + 4 = 2x + 9 --- ✏️ Step 1: Move variables to one side Subtract 2x from both sides: 3x - 2x + 4 = 2x - 2x + 9 x + 4 = 9 --- ✏️ Step 2: Move constants to the other side Subtract 4 from both sides: x + 4 - 4 = 9 - 4 x = 5 --- ✅ Final Answer: x = 5 --- 📝 Quick Tip: Always move all the x terms to one side and the numbers to the other before solving. Then simplify step-by-step. --- 🔗 Follow for more: 🌐 Website: www.easymath sguid.com.ng 📘 Blog: easymathsteps.blogspot.com