Solving Absolute Value Equations

This video tutorial covers solving absolute value equations involving quadratic and rational expressions. It begins with a review of basic absolute value equations and introduces a rule for solving them. The tutorial then explores special cases, such as when the absolute value equals zero or a negative number. It provides examples of solving equations with quadratic and rational expressions, emphasizing the importance of isolating the absolute value operation. The video concludes with a discussion on handling equations with two absolute value operations.

What is the main focus of this lesson on absolute value equations?

• Graphing absolute value functions

• Solving inequalities

• Solving quadratic and rational expressions

• Solving linear equations

When solving an absolute value equation, if the absolute value is set equal to a positive number, what are the possible solutions?

• The expression equals zero or a negative number

• The expression equals the positive number only

• The expression equals the positive number or zero

• The expression equals the positive number or its negative

In the example of solving the equation |2x - 5| = 3, what are the solutions for x?

• x = 3 or x = -3

• x = 4 or x = -1

• x = 5 or x = -5

• x = 4 or x = 1

What happens when the absolute value is set equal to zero?

• There are no solutions

• The expression inside the absolute value must be zero

• The expression inside the absolute value can be any number

• The expression inside the absolute value must be positive

How do you solve an absolute value equation involving a quadratic expression?

• By factoring the expression only

• By using the quadratic formula only

• By setting the expression equal to the positive and negative of the number

• By graphing the equation

What is the solution to the equation |x^2 - 5x| = 6?

• x = 5 or x = -2

• x = 4 or x = 1

• x = 2 or x = 3

• x = 6 or x = -1

When solving an absolute value equation with a rational expression, what is the first step?

• Isolate the absolute value operation

• Add a constant to both sides

• Subtract a constant from both sides

• Multiply both sides by the denominator

In equations with two absolute value operations set equal, what are the possible scenarios?

• The expressions are equal or one is the negative of the other

• The expressions are both zero

• The expressions are both positive

• The expressions are both negative