Ilustrasi Masalah Persamaan Linear Satu Variabel (PLVS)

Introduction

This tutorial is designed to help you understand and illustrate problems related to linear equations with one variable. Linear equations are foundational concepts in algebra and are essential for solving various mathematical and real-world problems. By the end of this guide, you will be able to set up and solve linear equations effectively.

Step 1: Understand Linear Equations

• A linear equation in one variable can be expressed in the form:

  ax + b = 0
  

  where:

  • a is a non-zero coefficient,
  • x is the variable,
  • b is a constant.

• Familiarize yourself with the terms:

  • Coefficient: The numerical factor in front of the variable (e.g., in 3x, 3 is the coefficient).
  • Constant: The term without a variable (e.g., in 3x + 5, 5 is the constant).

Step 2: Set Up the Equation

• Identify the problem you need to solve and express it as an equation.
• Example problem: "The sum of twice a number and 4 equals 10."
  • Translate this into an equation:

    2x + 4 = 10
    

Step 3: Isolate the Variable

• To solve for x, you need to isolate it on one side of the equation. Follow these sub-steps:
  1. Subtract the constant from both sides:

     2x + 4 - 4 = 10 - 4
     

     This simplifies to:

     2x = 6
     

  2. Divide both sides by the coefficient of x:

     x = 6 / 2
     

     This results in:

     x = 3
     

Step 4: Verify Your Solution

• Always check your solution by substituting it back into the original equation.
  • Substitute x = 3 into the original equation:

    2(3) + 4 = 10
    

  • Simplifying the left side gives:

    6 + 4 = 10
    

  • Since both sides are equal, the solution is verified.

Step 5: Practice with Different Problems

• To solidify your understanding, practice with various problems. Try creating equations from word problems or simple statements.
• Example: "Five times a number decreased by 7 equals 18."
  • Set up the equation:

    5x - 7 = 18
    

Conclusion

In this tutorial, you learned how to illustrate and solve problems involving linear equations with one variable. Key steps include understanding the structure of linear equations, setting them up based on word problems, isolating the variable, and verifying your solution. For further practice, tackle more complex equations or explore systems of equations as your next steps.