Solving Absolute Value Inequalities Challenge

This video tutorial covers absolute value inequalities, explaining different scenarios and how to solve them. It includes examples demonstrating how to solve, graph, and express solutions in interval notation. The video emphasizes understanding when solutions are all real numbers or no solution, using a reference table to guide the process.

If the absolute value of a number is greater than a positive number, what type of inequality is used?

• Not equal to inequality

• Approximately equal to inequality

• Or inequality

• And inequality

What is the solution when the absolute value of a number is greater than a negative number?

• Only negative numbers

• Only positive numbers

• No solution

• All real numbers

When the absolute value of a number is less than a positive number, how is the inequality solved?

• As an 'or' inequality

• As an 'and' inequality

• As an 'approximately equal to' inequality

• As a 'not equal to' inequality

What is the solution when the absolute value of a number is less than a negative number?

• No solution

• All real numbers

• Only positive numbers

• Only negative numbers

What are the four types of inequalities discussed in the video?

• Greater than, less than, equal to, not equal to

• Greater than, less than, greater than or equal to, less than or equal to

• Greater than, less than, approximately equal to, not equal to

• Greater than, less than, equal to, approximately equal to

In Example 1, what is the first step to solve the inequality 2x + 3 > 2?

• Divide by 2

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply by 2

In Example 1, what is the interval notation for the solution?

• (-∞, -5/2) ∪ (1/2, ∞)

• (-∞, -1/2) ∪ (5/2, ∞)

• (-∞, -1/2) ∪ (5/2, ∞)

• (-∞, -5/2) ∪ (1/2, ∞)

In Example 2, what is the inequality after subtracting 2 from both sides?

• 7x - 4 < 9

• 7x - 4 ≥ 9

• 7x - 4 ≤ 9

• 7x - 4 > 9

In Example 3, what happens to the inequality sign when dividing by a negative number?

• It stays the same

• It becomes an 'and' inequality

• It switches direction

• It becomes an 'or' inequality

In Example 4, what is the solution when the absolute value is greater than a negative number?

• All real numbers

• Only negative numbers

• No solution

• Only positive numbers