Pertidaksamaan Linear Satu Variabel | Pengetahuan Kuantitatif | Alternatifa

Introduction

This tutorial focuses on understanding and solving linear inequalities in one variable, a fundamental concept in quantitative knowledge. Mastering this topic will enhance your problem-solving skills and prepare you for more advanced mathematical concepts.

Step 1: Understanding Linear Inequalities

Begin by familiarizing yourself with what a linear inequality is.

• A linear inequality relates two expressions using inequality signs such as <, >, ≤, or ≥.
• It can be expressed in the form:
  • ax + b < c
  • ax + b > c
  • ax + b ≤ c
  • ax + b ≥ c

Where:

• a, b, and c are constants
• x is the variable

Practical Advice

• Remember that the solution to a linear inequality is a range of values for x that satisfy the inequality.

Step 2: Graphing Linear Inequalities

Visual representation can help in understanding the solutions of inequalities.

• Start with the equation form (replace the inequality sign with an equal sign).
• Graph the corresponding line on a coordinate plane.
• Use a solid line for ≤ or ≥ and a dashed line for < or >.
• Shade the region that satisfies the inequality.

Practical Advice

• Test a point not on the line to determine which side of the line to shade. If the point satisfies the inequality, shade that side.

Step 3: Solving Linear Inequalities Algebraically

Follow these steps to solve linear inequalities algebraically:

1. Isolate the variable: Use inverse operations to get x alone on one side.

   • Example: For 2x + 3 < 7, subtract 3 from both sides:
     • 2x < 4

2. Divide by the coefficient of x:

   • Continuing the example:
     • x < 2

3. Consider the inequality sign: If you multiply or divide by a negative number, flip the inequality sign.

Common Pitfalls

• Always check your final solution by substituting values back into the original inequality.

Step 4: Writing and Interpreting Solutions

Express the solution of the inequality in interval notation.

• For example, x < 2 can be written as:
  • (-∞, 2)

Real-World Application

Understanding intervals can be useful in various fields such as economics, engineering, and data analysis, where constraints and limits are common.

Conclusion

In this tutorial, you learned the basics of linear inequalities, how to graph them, solve them algebraically, and express their solutions in interval notation. Practicing these steps will enhance your quantitative skills and prepare you for more complex mathematical challenges. To further your understanding, consider exploring systems of inequalities or real-world applications of these concepts.