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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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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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Graphing Inequalities on a Number Line

 Graphing Inequalities on a Number Line Visualizing inequalities on a number line helps us understand which values satisfy an inequality. This lesson shows you how to graph them step by step. --- 🔸 How to Graph an Inequality Steps to follow: 1. Draw a number line 2. Mark the value in the inequality 3. Use: Open circle (○) for or — value not included Closed circle (●) for or — value included 4. Shade the direction: Left for less than Right for greater than --- ✅ Example 1: Graph  Open circle at 4 Shade to the left <=========○---------  4 ✅ Final Answer: x < 4 --- ✅ Example 2: Graph  Closed circle at –2 Shade to the right --------●=========> -2 ✅ Final Answer: x ≥ –2 --- 🔸 Quick Summary: Symbols and Circles Symbol Type of Dot Includes the Number?  or Open circle (○) ❌ No  or Closed circle (●) ✅ Yes 📝 Practice Questions: Practice: Graph the following inequalities on a number line. 1. x > 2 2. x ≤ 0 3. x ≥ –5 4. x < –1 5. x ≥ 7 📘 Keep l...
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