Exploring Absolute Value Equations

Mr. Allen introduces solving absolute value equations by splitting them into two separate equations. He demonstrates solving 2x - 7 = 11 and 2x - 7 = -11, explaining the logic behind setting the equation to negative values. Each solution is verified by substituting back into the original equation. The video concludes with a reminder to check solutions.

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

• Combine like terms

• Isolate the absolute value expression

• Distribute any constants

• Factor the equation

Why do we split the absolute value equation into two separate equations?

• To solve for both positive and negative scenarios

• To eliminate the absolute value

• To check for extraneous solutions

• To simplify the equation

What are the two equations derived from the absolute value equation |2x - 7| = 11?

• 2x - 7 = 11 and 2x + 7 = 11

• 2x + 7 = 11 and 2x - 7 = 11

• 2x - 7 = 11 and 2x - 7 = -11

• 2x + 7 = 11 and 2x + 7 = -11

What is the solution to the equation 2x - 7 = 11?

• x = 9

• x = -2

• x = 2

• x = -9

What is the absolute value of -11?

• 11

• -11

• 0

• 1

What is the absolute value of 11?

• 11

• -11

• 0

• 1

What is the value of x when solving 2x - 7 = -11?

• x = 9

• x = 2

• x = -2

• x = -9

What is the result of 2 times -2 minus 7?

• 11

• 9

• -11

• -9

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

• To simplify the equation further

• To ensure the solutions are within the domain

• To find extraneous solutions

• To verify that the solutions satisfy the original equation