Exploring One-Variable Absolute Value Equations and Inequalities

This video tutorial provides a comprehensive overview of solving absolute value equations and inequalities. It begins with an introduction to absolute value equations, followed by detailed examples demonstrating the step-by-step process of solving them. The tutorial also covers cases where no solution exists. The second part of the video introduces absolute value inequalities, offering examples and discussing special cases. The tutorial emphasizes understanding the concepts and applying them to solve various problems.

What is the first step in solving the equation 3|4x - 5| - 2 = 19?

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 2 from both sides

• Add 2 to both sides

After isolating the absolute value in the equation 3|4x - 5| = 21, what are the two possible values inside the absolute value?

• 21 and -21

• 7 and -7

• 5 and -5

• 4 and -4

In the equation |4x - 5| = 7, what are the solutions for x?

• x = 2 and x = -2

• x = 5 and x = -5

• x = 3 and x = -1/2

• x = 1 and x = -1

What is the first step in solving the equation |-(x + 4/3)/2| = 6?

• Subtract 1 from both sides

• Add 1 to both sides

• Multiply both sides by 2

• Divide both sides by 2

What is the solution to the equation |-(x + 4/3)/2| = 6?

• x = 12 and x = -12

• x = 4 and x = -4

• x = 32/3 and x = -40/3

• x = 6 and x = -6

What does it mean if an absolute value equation equals a negative number?

• There are infinite solutions

• There is no solution

• There are two solutions

• There is one solution

What is an extraneous solution?

• A solution that satisfies the original equation

• A solution that satisfies the inequality

• A solution that does not satisfy the original equation

• A solution that satisfies a simplified version of the equation

When solving the inequality |4 - 2x| ≤ 22, what compound inequality should be set up?

• 4 - 2x ≤ 22

• -22 ≤ 4 - 2x ≤ 22

• 4 - 2x ≥ -22

• -22 ≤ 2x - 4 ≤ 22

What happens to the inequality symbol when you divide both sides by a negative number?

• It stays the same

• It flips direction

• It becomes an equal sign

• It becomes a less than sign

What does it mean if an absolute value inequality is always true?

• There are infinite solutions

• There is one solution

• There is no solution

• There are two solutions