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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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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 Word Problems Involving Fractions in Equations

This lesson shows how to solve real-world problems where fractions are involved in the equation. It builds directly from Lesson 12 on dividing fractions. --- 🔍 Steps to Solve: 1. Read the word problem carefully. 2. Let the unknown number be x. 3. Translate the words into a fraction-based equation. 4. Solve by multiplying by the reciprocal or using the LCM method. 5. State your final answer clearly. --- 📘 Example 1: Problem: One-third of a number is 9. What is the number? Solution: Let the number be x. (1/3) × x = 9 Multiply both sides by 3: x = 9 × 3 = 27 ✅ Final Answer: 27 --- 📘 Example 2: Problem: Half a number minus 2 equals 3. Find the number. Solution: (1/2) × x - 2 = 3 Add 2 to both sides: (1/2) × x = 5 Multiply both sides by 2: x = 10 ✅ Final Answer: 10 --- 📘 Example 3: Problem: Two-thirds of a number equals 16. What is the number? Solution: (2/3) × x = 16 Multiply both sides by 3/2: x = 16 × (3/2) = 48/2 = 24 ✅ Final Answer: 24 --- 📝 Practice Questions: 1. One-fourth of a ...
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