Exploring Absolute Value Equations

Mr. Allen explains how to solve an absolute value equation. The process involves isolating the absolute value expression, splitting it into two separate equations, solving each equation, and verifying the solutions by substitution. The video provides a step-by-step guide to ensure understanding and accuracy in solving such equations.

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

• Subtract a constant from both sides

• Multiply both sides by a constant

• Isolate the absolute value part

• Add a constant to both sides

After isolating the absolute value, what should be done next?

• Combine like terms

• Split the equation into two separate equations

• Square both sides

• Take the square root of both sides

What are the two equations obtained from |x + 4| = 5?

• x - 4 = 5 and x - 4 = -5

• x + 4 = 5 and x - 4 = 5

• x + 4 = 0 and x - 4 = 0

• x + 4 = 5 and x + 4 = -5

How do you solve the equation x + 4 = 5?

• Add 4 to both sides

• Multiply both sides by 4

• Divide both sides by 4

• Subtract 4 from both sides

What is the solution to the equation x + 4 = -5?

• x = -1

• x = -9

• x = 1

• x = 9

What is the result of plugging x = 1 back into the original equation?

• 10

• 5

• 20

• 15

What is the result of plugging x = -9 back into the original equation?

• 10

• 5

• 15

• 20