Solving Absolute Value Inequalities

This video tutorial covers solving absolute value inequalities, explaining the rules and methods for handling these problems. It discusses the differences between less than and greater than inequalities, provides examples, and demonstrates how to solve and graph them. The tutorial also addresses complex problems and special cases, such as when there is no solution or when all real numbers are solutions.

What is the main difference between solving absolute value inequalities and regular inequalities?

• Absolute value inequalities do not have any special rules.

• Absolute value inequalities use different symbols.

• Absolute value inequalities require considering both positive and negative solutions.

• Absolute value inequalities are solved using only addition and subtraction.

When solving an absolute value inequality of the form |K| < a, what does 'a' represent?

• The maximum value of K.

• The distance from zero on the number line.

• The minimum value of K.

• The midpoint of the inequality.

In the inequality |K| < 8, which of the following is true?

• K must be exactly 8.

• K must be between -8 and 8.

• K must be less than -8 or greater than 8.

• K can be any number greater than 8.

For the inequality |K| > a, what type of statement is used to express the solution?

• An 'and' statement.

• A 'but' statement.

• An 'or' statement.

• A 'not' statement.

In the inequality |K| > 8, which of the following is true?

• K must be exactly 8.

• K can be any number less than 8.

• K must be less than -8 or greater than 8.

• K must be between -8 and 8.

What is the solution to the inequality |X + 2.8| ≤ 10.4?

• -7.6 ≤ X ≤ 7.6

• X ≤ -7.6 or X ≥ 7.6

• -10.4 ≤ X ≤ 2.8

• X ≤ -10.4 or X ≥ 2.8

How do you solve the inequality |X/5| > 1?

• Multiply both sides by 5 and solve for X.

• Divide both sides by 5 and solve for X.

• Add 5 to both sides and solve for X.

• Subtract 5 from both sides and solve for X.

What is the solution to the inequality |X - 10| < 12?

• -2 < X < 22

• X < -12 or X > 2

• -12 < X < 2

• X < -2 or X > 22

What happens if you have an absolute value inequality with a negative number on the other side, such as |X + 21| ≤ -7?

• The solution is X = -7.

• The solution is X = 21.

• The solution is all real numbers.

• There is no solution.

What is the solution to the inequality |X + 33| > -24?

• All real numbers.

• No solution.

• X = 33.

• X = -24.