8TH EDITION | BOOK 2 | EXERCISE 3A | QUESTION # 1, 2, 3

Summary

In this educational video, Mahboob Ahmed walks students through a series of algebraic inequalities, providing step-by-step solutions and explanations. The video covers multiple exercises, from filling in inequality symbols to solving for variables, simplifying expressions, and representing solutions on number lines. Key concepts such as dividing and multiplying inequalities, handling rational numbers, and interpreting solutions with greater-than or less-than signs are emphasized. The tutorial is designed to help students build confidence in solving inequalities and improve their understanding of algebraic problem-solving techniques.

Takeaways

• 😀 The video introduces Mahboob Ahmed teaching math concepts through various inequality problems and solutions.
• 😀 The script covers multiple exercises, starting with solving MCQs involving inequalities like less than, greater than, and equal to signs.
• 😀 Part A explains the comparison of real numbers using inequalities, with a detailed example showing how to solve them step-by-step.
• 😀 In Part B, the script highlights how to manipulate inequalities, like simplifying expressions and using the correct inequality symbols when performing operations.
• 😀 Part C shows how to handle inequalities involving multiplication and division by numbers, explaining how to preserve or change inequality signs depending on the operation.
• 😀 The video also teaches about using the number line to represent solutions for inequalities, including open and closed bubbles for inequalities involving 'less than' or 'greater than'.
• 😀 Part D covers dividing and simplifying inequalities by negative numbers, stressing the importance of changing the inequality direction when dividing by a negative.
• 😀 Part E involves solving inequalities with fractions and prime numbers, offering clear steps to find solutions that satisfy the given conditions.
• 😀 The video also includes multiple problems involving rational numbers and finding the smallest or greatest possible value of a variable that satisfies the inequality.
• 😀 In conclusion, the script encourages students to practice with various types of inequalities and reinforces the importance of careful algebraic manipulation when solving them.

Q & A

What is the correct inequality symbol to use when dividing both sides of an inequality by a positive number?

When dividing both sides of an inequality by a positive number, the inequality symbol remains the same. For example, if the inequality is 'x < 7', dividing both sides by 4 results in 'x/4 < 7/4'.

How does dividing both sides of an inequality by a negative number affect the inequality symbol?

When dividing both sides of an inequality by a negative number, the inequality symbol must be reversed. For example, if the inequality is 'x > 5', dividing both sides by -2 changes it to 'x < -2.5'.

In the example '5 - k' and '7 - k', how can we determine the correct inequality symbol?

By substituting a value for 'k', such as k = 1, we simplify the two expressions. After simplifying, we see that '4' is smaller than '6', so the correct inequality symbol between '5 - k' and '7 - k' is '<'.

Why is it important to use an open bubble when representing an inequality like 'x < 7' on the number line?

An open bubble is used to indicate that the value of 'x' does not include 7. This is because the inequality 'x < 7' means 'x' is less than 7 but does not equal 7.

What does the notation 'x ≥ 7' represent on a number line?

'x ≥ 7' means that 'x' can be any value greater than or equal to 7. On a number line, this is represented by a solid bubble at 7 and a shaded arrow extending to the right to indicate all values greater than 7 are included.

How do you represent the solution for 'x < -3' on a number line?

For 'x < -3', the number line should have an open bubble at -3 (indicating it is not included), and an arrow to the left of -3 showing all values less than -3 are solutions.

In the expression 'x > y', how do we solve for 'x' when 'y' is given?

To solve for 'x' in the inequality 'x > y', simply perform the required algebraic operations to isolate 'x'. If 'y' is a number, you may add, subtract, multiply, or divide both sides of the inequality, making sure to adjust the inequality symbol as necessary (e.g., reversing it when multiplying/dividing by a negative number).

What is the smallest rational number that satisfies the inequality '8 ≤ 7x'?

To solve '8 ≤ 7x', divide both sides by 7 to get 'x ≥ 8/7'. The smallest rational number that satisfies this inequality is 8/7.

What is the smallest prime number 'x' that satisfies the inequality '20x > 33'?

To solve '20x > 33', divide both sides by 20 to get 'x > 33/20'. The smallest prime number greater than 33/20 (which is approximately 1.65) is 2, so the smallest prime number satisfying this inequality is 2.

What happens when we solve the inequality '3x > 105' by dividing both sides by 3?

When dividing '3x > 105' by 3, we get 'x > 35'. This inequality means that 'x' can be any value greater than 35. The largest integer solution would be the smallest integer greater than 35, which is 36.