Understanding Absolute Value Equations

The video tutorial explains how to solve absolute value equations by first isolating the absolute value on one side of the equation. It then demonstrates setting up and solving two separate equations based on the absolute value principle. The tutorial concludes by checking the solutions to ensure they are correct.

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

• Check the solutions

• Multiply both sides by 6

• Add 3 to both sides

• Isolate the absolute value

How do you isolate the absolute value in the equation 6|2x + 3| + 3 = 63?

• Divide both sides by 6, then add 3

• Subtract 3 from both sides, then divide by 6

• Add 3 to both sides, then multiply by 6

• Multiply both sides by 6, then subtract 3

What principle is used to set up two equations from an absolute value equation?

• The principle of addition

• The principle of subtraction

• The principle of absolute value

• The principle of multiplication

What are the two equations derived from |2x + 3| = 10?

• 2x + 3 = 10 and 2x + 3 = -10

• 2x - 3 = 10 and 2x + 3 = 10

• 2x - 3 = 10 and 2x - 3 = -10

• 2x + 3 = 10 and 2x - 3 = 10

What is the solution to the equation 2x + 3 = 10?

• x = 10

• x = 5

• x = 7/2

• x = 3

What is the solution to the equation 2x + 3 = -10?

• x = -13/2

• x = -5

• x = -7

• x = -3

What are the solutions to the absolute value equation 6|2x + 3| + 3 = 63?

• x = 10 and x = -10

• x = 3 and x = -3

• x = 7/2 and x = -13/2

• x = 5 and x = -5

Why is it recommended to check the solutions of an absolute value equation?

• To ensure they satisfy the original equation

• To simplify the equation further

• To find more solutions

• To eliminate incorrect solutions

What is the final step after solving the absolute value equations?

• Multiply the solutions by 2

• Divide the solutions by 2

• Check the solutions

• Add the solutions together