Solving Absolute Value Equations

The video tutorial covers solving absolute value equations, starting with the basic concept of absolute value as a number's distance from zero. It explains how to solve these equations by isolating the absolute value and creating two separate equations. The tutorial also addresses extraneous solutions and demonstrates how to verify solutions. Advanced problem-solving techniques are discussed, and the video concludes with applying absolute value to real-world word problems, such as estimating house costs.

What is the absolute value of -5?

• -5

• 0

• 5

• 10

If the absolute value of x equals 5, what are the possible values of x?

• 5 and -5

• 5 and 0

• 0 and -5

• 5 and 10

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

• Square both sides

• Get the absolute value by itself

• Add a constant to both sides

• Multiply both sides by a constant

Solve the equation: |2x - 9| = 15. What are the solutions for x?

• x = 12 and x = -3

• x = 12 and x = 3

• x = -12 and x = -3

• x = -12 and x = 3

What is an extraneous root?

• A root that is always positive

• A root that does not satisfy the equation

• A root that is always negative

• A root that satisfies the equation

Why do we check for extraneous roots in absolute value equations?

• To simplify the equation

• To verify the solutions are correct

• To find additional solutions

• To eliminate negative solutions

Solve the equation: |4x + 10| = 6x. What is the valid solution for x?

• x = 6

• x = -1

• x = -2

• x = 5

In the equation |2x + 12| = 4x, what is the correct solution for x?

• x = 6

• x = -2

• x = 8

• x = -6

What is the maximum cost of the house if the estimated cost is $250,000 with a margin of $30,000?

• $280,000

• $220,000

• $300,000

• $250,000

What is the minimum cost of the house if the estimated cost is $250,000 with a margin of $30,000?

• $300,000

• $250,000

• $220,000

• $280,000