Kurikulum Merdeka Matematika Kelas 8 Bab 3 Persamaan dan Pertidaksamaan Linier Satu Variabel

Summary

In this educational video, the instructor provides a comprehensive overview of linear equations and inequalities in one variable for 8th-grade mathematics. The session begins by distinguishing between open and closed statements, before delving into the structure and solving methods for linear equations. The instructor illustrates key concepts with examples, making complex ideas accessible. The video then transitions to linear inequalities, emphasizing the importance of inequality symbols and their manipulation. Practical examples are provided to reinforce understanding, ensuring students grasp essential mathematical principles while maintaining engagement throughout the lesson.

Takeaways

• 😀 Open sentences are expressions with uncertain values (e.g., 3 - P = 2).
• 😀 Closed sentences are expressions with definite values (e.g., Indonesia's Independence Day is August 17).
• 📏 Linear equations in one variable contain only one variable, such as A in 2A + 3.
• 🔍 Solving linear equations involves isolating the variable (e.g., a + 5 = 4 results in a = -1).
• 🔄 When moving numbers across the equation, change their sign (e.g., from +5 to -5).
• ✅ Inequalities use symbols like <, >, ≤, and ≥ to show relationships between values.
• 📊 The solving process for inequalities is similar to equations, but reverse the inequality sign when multiplying or dividing by a negative.
• 📈 Example: Solving x + 3 > 16 gives x > 13 (solution set includes 14, 15, etc.).
• 🔢 Example: Solving x - 4 < 2 gives x < 6 (solution set includes 5, 4, etc.).
• ⚖️ Example: In -2x + 5 < 7, isolating x leads to x > -1 (solution set includes 0, 1, etc.).

Q & A

What is the difference between an open sentence and a closed sentence?

An open sentence is a statement with an uncertain value, such as '3 - P = 2', where the value of P is unknown. A closed sentence has a definite value, like 'Independence Day in Indonesia is on August 17'.

What is the general form of a linear equation in one variable?

A linear equation in one variable contains only one type of variable. For example, in the expression '2A + 3', A is the only variable.

How do you solve the equation A + 5 = 4?

To solve A + 5 = 4, subtract 5 from both sides, giving A = 4 - 5, which simplifies to A = -1.

What is the solution for the equation 6 = A - 3?

To solve 6 = A - 3, add 3 to both sides to get A = 6 + 3, which simplifies to A = 9.

How do you isolate X in the equation 2X - 8 = 16?

First, add 8 to both sides to get 2X = 16 + 8, which simplifies to 2X = 24. Then, divide both sides by 2 to find X = 12.

What symbols are used in linear inequalities?

Linear inequalities use symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

How do you solve the inequality X + 3 > 16?

To solve X + 3 > 16, subtract 3 from both sides, resulting in X > 16 - 3, which simplifies to X > 13.

What is the solution set for the inequality X - 4 < 2?

To solve X - 4 < 2, add 4 to both sides to get X < 2 + 4, simplifying to X < 6. The solution set includes values like 5, 4, 3, etc.

What happens to the inequality symbol when multiplying or dividing by a negative number?

When multiplying or dividing both sides of an inequality by a negative number, the inequality symbol reverses. For example, if you have -2X < 4 and divide by -2, it changes to X > -2.

What is the solution for the inequality -2X + 5 < 7?

To solve -2X + 5 < 7, first subtract 5 from both sides to get -2X < 7 - 5, which simplifies to -2X < 2. Then, divide by -2, reversing the inequality symbol to get X > -1.