How to Solve Compound Inequalities
Solving Compound Inequalities Compound inequalities are two inequalities joined by "and" or "or". They describe a range of values that satisfy both or either condition. --- 🔸 Types of Compound Inequalities 1. “And” Compound Inequality – Both conditions must be true – The solution is where the two inequalities overlap Example: 1 < x ≤ 5 Means x is greater than 1 and less than or equal to 5 2. “Or” Compound Inequality – Either condition can be true – The solution includes both sides Example: x < –3 or x > 2 --- ✅ Example 1: Solve 1 < x + 2 ≤ 5 Step 1: Split into two parts: – 1 < x + 2 – x + 2 ≤ 5 Step 2: Solve each: – 1 < x + 2 → Subtract 2 → –1 < x – x + 2 ≤ 5 → Subtract 2 → x ≤ 3 ✅ Final Answer: –1 < x ≤ 3 --- ✅ Example 2: Solve x – 4 < –1 or x + 2 > 7 Step 1: Solve both parts: – x – 4 < –1 → Add 4 → x < 3 – x + 2 > 7 → Subtract 2 → x > 5 ✅ Final Answer: x < 3 or x > 5 Summary of Compound Inequalities Type: "...