Kelas 10 SMA - Matematika - Sistem Pertidaksamaan Linear - Bimbel Tridaya Online

Introduction

This tutorial covers the fundamental concepts of linear inequalities, which are essential in mathematics, especially for high school students. Understanding these concepts will help you solve problems involving inequalities and graph them accurately.

Step 1: Understanding Linear Inequalities

• Definition: A linear inequality is similar to a linear equation but uses inequality symbols (>, <, ≥, ≤) instead of an equal sign.
• Example:
  • Linear equation: 2x + 3 = 7
  • Linear inequality: 2x + 3 > 7

Key Points

• The solution to a linear inequality describes a range of values rather than a single value.
• You can graph the solutions on a number line or coordinate plane.

Step 2: Identifying Inequality Symbols

• Learn the meaning of each symbol:
  • > means "greater than."
  • < means "less than."
  • ≥ means "greater than or equal to."
  • ≤ means "less than or equal to."

Practical Tips

• Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

Step 3: Solving Linear Inequalities

1. Isolate the variable: Similar to solving linear equations, aim to get the variable on one side.
   • Example: Solve 3x - 4 < 5
     • Add 4 to both sides: 3x < 9
     • Divide by 3: x < 3
2. Graph the solution:
   • Use an open circle for < or >.
   • Use a closed circle for ≤ or ≥.
   • Draw an arrow to indicate the range of solutions.

Step 4: Solving Compound Inequalities

• Compound inequalities involve two inequalities joined by "and" or "or."
• Example: Solve the compound inequality 1 < 2x + 3 ≤ 7.
  1. Break it into two parts:
     • 1 < 2x + 3
     • 2x + 3 ≤ 7
  2. Solve each part:
     • From 1 < 2x + 3: Subtract 3 → -2 < 2x → -1 < x (divide by 2)
     • From 2x + 3 ≤ 7: Subtract 3 → 2x ≤ 4 → x ≤ 2 (divide by 2)
  3. Combine the results: -1 < x ≤ 2

Step 5: Real-World Applications

• Linear inequalities can model various real-world situations, such as budget constraints, distance, and resource allocation.
• Practice applying these concepts to scenarios like:
  • Determining the maximum number of items you can buy within a budget.
  • Analyzing speed limits in traffic scenarios.

Conclusion

Understanding linear inequalities is crucial for solving mathematical problems and applying them in real life. Practice solving different types of inequalities and graphing their solutions to reinforce your skills. For further assistance or personalized tutoring, consider reaching out to educational resources such as Tridaya Online. Keep practicing and exploring the applications of linear inequalities to enhance your understanding.