CARA MUDAH PERSAMAAN DAN PERTIDAKSAMAAN LINEAR SATU VARIABEL

Introduction

This tutorial will guide you through the process of solving linear equations and inequalities with one variable. Understanding these mathematical concepts is crucial for tackling more complex problems in algebra and is widely applicable in various fields, including engineering, economics, and everyday problem-solving.

Step 1: Understanding Linear Equations

• A linear equation in one variable takes the form:

  ax + b = 0
  

  where a and b are constants and x is the variable.
• To solve for x, isolate it on one side of the equation:
  • Subtract b from both sides:

    ax = -b
    

  • Divide both sides by a:

    x = -b/a
    

• Practical Tip: Always check your solution by substituting x back into the original equation.

Step 2: Solving Linear Inequalities

• A linear inequality looks similar to a linear equation but uses inequality signs (>, <, ≥, ≤). For example:

  ax + b > c
  

• To solve, follow these steps:
  • Isolate the variable on one side:
    • Subtract b from both sides:

      ax > c - b
      

    • Divide by a:

      x > (c - b)/a
      

  • Important: If you multiply or divide by a negative number, reverse the inequality sign.
• Common Pitfall: Ensure you apply the correct sign when dealing with negative numbers.

Step 3: Graphing Linear Equations and Inequalities

• Graphing Linear Equations:

  • Identify the slope (m) and y-intercept (b) from the equation y = mx + b.
  • Plot the y-intercept on the graph.
  • Use the slope to find another point and draw a line through both points.

• Graphing Linear Inequalities:

  • Convert the inequality to slope-intercept form if necessary.
  • Graph the boundary line (use a dashed line for < and >, solid for ≤ and ≥).
  • Shade the appropriate area that satisfies the inequality.

Step 4: Applying the Concepts

• Practice solving various linear equations and inequalities to reinforce your understanding.
• Use real-world scenarios to apply your skills, such as calculating budget constraints or analyzing trends.

Conclusion

In this tutorial, we've covered the fundamentals of solving linear equations and inequalities in one variable. Key takeaways include isolating the variable, understanding the implications of inequality signs, and effectively graphing solutions. For further practice, explore more complex equations or start applying these concepts to real-world situations.