Solving Absolute Value Equations

The video tutorial explains how to solve absolute value equations by isolating the absolute value expression, solving the resulting equations, and verifying the solutions. It emphasizes the importance of considering both positive and negative solutions due to the nature of absolute values. The tutorial concludes with tips on handling such equations effectively.

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

• Distribute any coefficients

• Add constants to both sides

• Combine like terms

• Isolate the absolute value function

Why is it important to isolate the absolute value function before solving?

• To simplify the equation

• To ensure the equation is linear

• To make it easier to graph

• To correctly set up two separate equations

What operation is performed to remove a constant from one side of the equation?

• Addition

• Subtraction

• Multiplication

• Division

After isolating the absolute value function, what is the next step?

• Combine like terms

• Set up two separate equations

• Graph the equation

• Check for extraneous solutions

What are the two equations derived from the absolute value equation |x + 8| = 10?

• x + 8 = 10 and x - 8 = 10

• x + 8 = 10 and x - 8 = -10

• x - 8 = 10 and x - 8 = -10

• x + 8 = 10 and x + 8 = -10

How do you solve the equation x + 8 = 10?

• Multiply both sides by 8

• Divide both sides by 8

• Subtract 8 from both sides

• Add 8 to both sides

What is the solution to the equation x + 8 = -10?

• x = 18

• x = 2

• x = -18

• x = -2

Why is it necessary to check the solutions in the original equation?

• To find the domain

• To simplify the equation

• To ensure they are not extraneous

• To graph the solutions

What is the absolute value of -10?

• 10

• 20

• -10

• 0

What should you do after solving the two separate equations?

• Graph the solutions

• Simplify the solutions

• Check the solutions in the original equation

• Combine the solutions