Understanding Absolute Values

The video tutorial covers solving absolute value equations, starting with an introduction to the concept of absolute value as a measure of distance from zero. It outlines the steps to solve such equations, including isolating the absolute value expression, setting up two equations, solving them, and checking for extraneous solutions. Two examples are provided to illustrate the process, with a focus on ensuring solutions are valid and understanding when solutions are extraneous.

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

Which of the following is the first step in solving an absolute value equation?

• Set the inside equal to positive and negative values

• Solve both equations

• Isolate the absolute value expression

• Check for extraneous solutions

When setting up equations for absolute value, what should you do with the inside value?

• Set it equal to the original equation

• Set it equal to zero

• Set it equal to both positive and negative values

• Set it equal to the absolute value

In the example of solving |X + 12| = 9, what are the two possible solutions for X?

• X = 3 and X = 21

• X = -3 and X = 21

• X = -3 and X = -21

• X = 3 and X = -21

Why is it important to check for extraneous solutions in absolute value equations?

• To simplify the equation further

• To ensure the solution is positive

• To verify the solution satisfies the original equation

• To find the smallest solution

In the equation |X + 10| = 4X - 8, what is the first step after isolating the absolute value?

• Subtract X from both sides

• Multiply both sides by 4

• Set up two equations

• Add 10 to both sides

What does it mean if a solution is considered extraneous?

• It is the only solution

• It does not satisfy the original equation

• It is a negative solution

• It is a repeated solution

In the second example, what is the value of X when solving the equation X + 10 = 4X - 8?

• X = 2

• X = -2

• X = 6

• X = -6

What is the result of dividing both sides by 5 in the equation 5X = -10?

• X = 5

• X = -5

• X = 2

• X = -2

Why might the teacher choose not to show the check for extraneous solutions in the second example?

• Because it is not necessary

• To save time

• Because the solution is obvious

• To avoid confusion with fractions