Persamaan dan Pertidaksamaan Linear

Introduction

This tutorial will guide you through the concepts of linear equations and inequalities in one variable, as discussed in the video "Persamaan dan Pertidaksamaan Linear". Understanding these concepts is essential for students in grade 10, especially in the context of the Indonesian educational curriculum. By the end of this tutorial, you will be able to solve linear equations and inequalities effectively.

Step 1: Understanding Linear Equations

Linear equations are mathematical statements that show the equality between two expressions. They typically have the following standard form:

• General form: ax + b = c
  • a, b, and c are constants
  • x is the variable

Practical Advice

• To solve for x, isolate it on one side of the equation:
  1. Subtract b from both sides: ax = c - b
  2. Divide both sides by a: x = (c - b) / a

Example

For the equation 3x + 5 = 20:

1. Subtract 5: 3x = 15
2. Divide by 3: x = 5

Step 2: Identifying Linear Inequalities

Linear inequalities express a relationship where one side is not necessarily equal to the other. The general form is similar to linear equations but uses inequality signs:

• General form: ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c

Practical Advice

• To solve linear inequalities, follow similar steps as for equations, but pay attention to the inequality sign when multiplying or dividing by a negative number, which reverses the sign.

Example

For the inequality 2x + 3 < 11:

1. Subtract 3: 2x < 8
2. Divide by 2: x < 4

Step 3: Graphing Linear Equations and Inequalities

Visual representation helps in understanding the solutions of linear equations and inequalities.

For Linear Equations

• Plot points that satisfy the equation on a graph.
• Connect the points with a straight line.

For Linear Inequalities

• Use a dashed line for inequalities that do not include equality (e.g., < or >).
• Use a solid line for inequalities that do include equality (e.g., ≤ or ≥).
• Shade the region that satisfies the inequality.

Step 4: Solving Word Problems Involving Linear Equations and Inequalities

Word problems can be translated into linear equations and inequalities.

Steps to Solve

1. Read the problem carefully and identify the variables.
2. Set up the equation or inequality based on the relationships described.
3. Solve for the variable.
4. Check the solution in the context of the problem.

Example

If a person has $10 and wants to buy pencils at $2 each, how many can they buy?
Set up the inequality: 2x ≤ 10 (where x is the number of pencils).

1. Divide by 2: x ≤ 5.
2. The person can buy a maximum of 5 pencils.

Conclusion

In this tutorial, we covered the basics of linear equations and inequalities, including how to solve them, graph them, and apply them to real-world scenarios. Mastering these concepts is crucial for further studies in mathematics. As a next step, practice solving different types of equations and inequalities to reinforce your understanding.