Solving Absolute Value Equations

The video tutorial explains how to solve absolute value equations. It begins with an introduction to absolute value and its properties, emphasizing the need to isolate the absolute value expression. The instructor sets up two cases for solutions, one positive and one negative, and demonstrates the steps to solve the equation. Finally, the solutions are converted into both decimal and fraction forms, highlighting the dual nature of absolute value solutions.

What is the first step in solving an absolute value equation?

• Multiply both sides by a constant

• Add a constant to both sides

• Isolate the absolute value expression

• Isolate the variable

Why is it important to isolate the absolute value expression?

• To simplify the equation

• To ensure the equation is balanced

• To prepare for solving two possible solutions

• To eliminate the variable

What does the absolute value of a number represent?

• The number itself

• The square of the number

• The negative of the number

• The distance from zero on a number line

How many solutions can an absolute value equation have?

• Three

• One

• None

• Two

What are the two cases set up for solving absolute value equations?

• Negative and zero

• Zero and undefined

• Positive and negative

• Positive and zero

What is the purpose of setting up two cases in solving absolute value equations?

• To account for both positive and negative scenarios

• To simplify the equation

• To find the average of solutions

• To verify the equation

In the first case, what operation is performed after adding one to both sides?

• Subtraction

• Multiplication

• Division

• Addition

What is the result of dividing 80 by -10 in the first case?

• 8

• -80

• 80

• -8

In the second case, what is the first step to isolate the variable?

• Divide by -10

• Multiply by -10

• Subtract one from both sides

• Add one to both sides

What is the result of dividing 78 by -10 in the second case?

• -78

• 7.8

• 78

• -7.8