← Chapter 54 Chapter 55: Inequalities Chapter 56 →

Chapter 55: Inequalities

✏️ Explanation

Inequalities show relationships using <, >, ≤, ≥. Solve like equations, but flip the inequality sign when multiplying/dividing by negative numbers.

< means "less than"
> means "greater than"
≤ means "less than or equal"
≥ means "greater than or equal"

🔍 Why It Matters

Inequalities model real constraints like budgets, capacity limits, and acceptable ranges.

✏️ Worked Example

Solve: 2x + 3 < 11
Step 1: Subtract 3 from both sides
2x + 3 - 3 < 11 - 3
2x < 8
Step 2: Divide both sides by 2
2x ÷ 2 < 8 ÷ 2
x < 4
⚠️ Remember: Only flip the inequality sign when multiplying or dividing by a negative number!

🔢 Practice Exercises

1. Solve: x + 5 > 12
2. Solve: 3y ≤ 15
3. Solve: 4 - x > 1
4. Solve: 2(x + 1) ≥ 10
5. List 3 integer solutions to x < 7

⚠️ Common Mistakes

  • Not flipping inequality with negative multiplication
  • Confusing < and ≤ symbols
  • Wrong direction on number lines

✨ Quick Summary

Solve like equations. Flip inequality sign when multiplying/dividing by negatives.