Understanding Absolute Value Inequalities

The video tutorial explains how to solve an inequality involving absolute values. It begins with a review of absolute value concepts, illustrating how to interpret inequalities on a number line. The tutorial then demonstrates solving the inequality by converting mixed numbers to improper fractions and eliminating fractions through multiplication. Finally, it validates the solution by testing values within the derived range, ensuring they satisfy the original inequality.

What does the absolute value of a number represent?

• The negative of the number

• The number itself

• The distance from zero on a number line

• The square of the number

If the absolute value of x is less than 2.5, which of the following is true?

• x is less than -2.5

• x is equal to 2.5

• x is greater than 2.5

• x is between -2.5 and 2.5

How do you convert a mixed number to an improper fraction?

• Multiply the whole number by the denominator and add the numerator

• Add the whole number to the numerator

• Multiply the numerator by the denominator

• Subtract the numerator from the whole number

What is the first step in solving the inequality 2r - 13/4 < 5/2?

• Subtract 5 from both sides

• Add 13 to both sides

• Multiply both sides by 4

• Divide both sides by 2

What is the solution range for r in the inequality 2r - 13/4 < 5/2?

• r < 2 and 7/8

• r < 3/8

• r > 3/8

• r > 2 and 7/8

What is the second condition that must be satisfied in the inequality problem?

• r must be greater than 2 and 7/8

• r must be less than 3/8

• r must be greater than 3/8

• r must be equal to 3/8

Which of the following values is a valid solution for r?

• r = 0

• r = 1

• r = 3

• r = 4

Why does r = 0 not satisfy the inequality?

• Because 0 is not a real number

• Because the absolute value of 0 is greater than 2 and 1/2

• Because 0 is less than 3/8

• Because 0 is greater than 2 and 7/8

What happens when you test r = 3 in the inequality?

• It is equal to the boundary

• It satisfies the inequality

• It does not satisfy the inequality

• It is not a real number

What is the purpose of testing values like 1, 0, and 3 in the solution?

• To find the exact solution

• To verify the solution range

• To determine the midpoint

• To calculate the average