Pertidaksamaan nilai mutlak video 4

Introduction

This tutorial focuses on solving absolute value inequalities involving addition and subtraction. Understanding these concepts is essential for mastering algebra and can be applied in various mathematical scenarios. We will break down the steps necessary to solve these inequalities clearly and concisely.

Step 1: Understand Absolute Value

• Absolute value represents the distance of a number from zero on the number line, regardless of direction.
• The absolute value of a number ( x ) is denoted as ( |x| ).
• For example:
  • ( |3| = 3 )
  • ( |-3| = 3 )

Step 2: Set Up the Inequality

• Create your absolute value inequality based on the problem statement.
• Example inequality:
  • ( |x + 2| < 5 )
• This means that the expression inside the absolute value can vary within a certain range.

Step 3: Break Down the Absolute Value Inequality

• To solve ( |a| < b ), split it into two inequalities:
  • ( -b < a < b )
• For our example ( |x + 2| < 5 ):
  • ( -5 < x + 2 < 5 )

Step 4: Solve the Compound Inequality

• Isolate ( x ) by solving the compound inequality:
  1. From ( -5 < x + 2 ):
     • Subtract 2 from both sides:
     • ( -5 - 2 < x ) results in ( -7 < x ) or ( x > -7 )
  2. From ( x + 2 < 5 ):
     • Subtract 2 from both sides:
     • ( x < 5 - 2 ) results in ( x < 3 )

Step 5: Combine the Results

• Combine the results from the inequalities:
  • The solution to the inequality ( |x + 2| < 5 ) is:
  • ( -7 < x < 3 )
• This means ( x ) can take any value between -7 and 3, not including -7 and 3.

Step 6: Practice with Other Inequalities

• Try solving similar inequalities to reinforce your understanding. Here are a few examples:
  • ( |x - 1| > 4 )
  • ( |2x + 3| \leq 6 )

Conclusion

In this tutorial, we've covered how to solve absolute value inequalities involving addition and subtraction. Remember to understand the absolute value concept, set up your inequalities correctly, break them down, solve the compound inequalities, and combine the results. Practice with various examples to strengthen your skills, and you will become proficient in handling these types of problems.