Understanding Absolute Value Equations

The video tutorial explains the concept of absolute value, emphasizing its role as the distance from zero. It details the process of solving absolute value equations by isolating the absolute value, presenting two cases (positive and negative), and checking solutions for accuracy. The tutorial highlights common mistakes and the importance of verifying solutions by substituting them back into the original equation.

What does the absolute value of a number represent?

• The square of the number

• The negative of the number

• The distance from zero

• The number itself

If the absolute value of -3 is calculated, what is the result?

• 6

• -3

• 3

• 0

What must the absolute value of a variable always be?

• Negative

• Undefined

• Positive

• Zero

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

• Add a constant to both sides

• Isolate the absolute value expression

• Multiply both sides by a constant

• Square both sides

When isolating the absolute value, which operation should be undone first?

• Multiplication

• Division

• Exponentiation

• Addition or subtraction

How many cases must be considered when solving an absolute value equation?

• Four

• Three

• Two

• One

What should you do to the other side of the equation when creating the negative case?

• Divide it by two

• Add a constant

• Negate it

• Square it

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

• Check the solutions

• Multiply both sides by a constant

• Add a constant to both sides

• Isolate the variable

Why is it important to check the solutions in an absolute value equation?

• To find the absolute value

• To simplify the equation

• To ensure they are positive

• To verify they satisfy the original equation

What should you do if the solution does not satisfy the original equation?

• Ignore it

• Multiply it by two

• Recalculate the solution

• Consider it invalid