Persamaan dan pertidaksamaan linear satu variabel

Introduction

This tutorial will guide you through the concepts of linear equations and inequalities in one variable. Understanding these concepts is crucial for solving mathematical problems and is foundational for more advanced math topics.

Step 1: Understanding Linear Equations

• A linear equation in one variable is of the form ax + b = 0, where:
  • a is a non-zero constant.
  • b is a constant.
  • x is the variable.
• To solve for x, follow these steps:
  1. Isolate the variable on one side of the equation.
  2. Perform operations to simplify the equation.

Example:

For the equation 2x + 4 = 0:

• Subtract 4 from both sides:
  • 2x = -4
• Divide by 2:
  • x = -2

Step 2: Understanding Linear Inequalities

• A linear inequality in one variable looks like ax + b < c (or ≤, >, ≥).
• The goal is to find the range of values for x that satisfy the inequality.
• To solve, follow these steps:
  1. Treat it like an equation to isolate x.
  2. Remember that if you multiply or divide by a negative number, you must reverse the inequality sign.

Example:

For the inequality 3x - 1 > 2:

• Add 1 to both sides:
  • 3x > 3
• Divide by 3:
  • x > 1

Step 3: Graphing Solutions

• Graphing helps visualize the solutions of linear equations and inequalities.
• For equations:
  • Plot the point on a number line where the equation holds true.
• For inequalities:
  • Use an open circle for < or >.
  • Use a closed circle for ≤ or ≥.
  • Shade the appropriate region to indicate the solution set.

Step 4: Common Pitfalls to Avoid

• Forgetting to reverse the inequality sign when multiplying or dividing by a negative number.
• Misplacing the variable when isolating it. Always perform the same operation on both sides of the inequality or equation.

Conclusion

In this tutorial, we covered the basics of linear equations and inequalities in one variable, including how to solve and graph them. Understanding these fundamental concepts will serve as a stepping stone for more complex mathematical topics. As a next step, practice solving various equations and inequalities to solidify your understanding.