Understanding Absolute Value Equations

The video tutorial explains how to solve absolute value equations by isolating the absolute value and setting up two equations based on the principle that absolute value represents distance from zero. It demonstrates solving two equations, verifying solutions through substitution, and applying these steps to a second equation where the absolute value is not initially isolated. The tutorial emphasizes the importance of verifying solutions to ensure correctness.

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

• Set up two equations

• Multiply by the reciprocal

• Isolate the absolute value

• Verify the solutions

What does the absolute value of a number represent?

• The number itself

• The negative of the number

• The square of the number

• The distance from zero

How many equations are set up from an absolute value equation?

• Three

• Four

• Two

• One

What is the solution to the equation 3x = 18?

• x = 12

• x = 9

• x = 6

• x = 3

Why is substitution used in verifying solutions?

• To find new solutions

• To eliminate variables

• To check if the solutions satisfy the original equation

• To simplify the equation

What is the reciprocal of two-thirds?

• Three halves

• One-third

• Two

• One-half

What operation is performed to isolate the absolute value in the second equation?

• Multiplication by the reciprocal

• Division

• Subtraction

• Addition

What are the solutions to the equation x = ±6?

• x = 0

• x = 3 and x = -3

• x = 12 and x = -12

• x = 6 and x = -6

How is the product of two-thirds and 6 simplified?

• By multiplying directly

• By subtracting the numbers

• By finding a common factor

• By adding the numbers

What is verified when 4 equals 4 in the context of the second equation?

• The equation needs modification

• The solution is correct

• The solution is incorrect

• The equation is incorrect