Solving Absolute Value Equations

The video tutorial covers solving absolute value equations, starting with an introduction to the concept of absolute value. It explains how to set up and solve equations by considering both positive and negative cases. The tutorial emphasizes the importance of checking solutions to ensure they are valid. It includes multiple examples to illustrate the process, including a case where no solution exists. The video concludes with homework instructions and a brief review of the key points.

What is the absolute value of -5?

• -5

• 0

• 5

• 10

Which of the following statements is true about absolute value?

• Absolute value is the same as the original number.

• Absolute value can be negative.

• Absolute value measures the distance from zero.

• Absolute value is always zero.

When solving absolute value equations, how many cases should you consider?

• Four

• One

• Three

• Two

In the equation |2x - 9| = 23, what are the two cases you need to solve?

• 2x + 9 = 23 and 2x + 9 = -23

• 2x - 9 = 23 and 2x + 9 = 23

• 2x - 9 = 23 and 2x - 9 = 0

• 2x - 9 = 23 and 2x - 9 = -23

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

• To find more solutions.

• To ensure the solutions are positive.

• To simplify the equation further.

• To verify that the solutions satisfy the original equation.

What should you do if one of the solutions does not satisfy the original equation?

• Change the original equation.

• Ignore it and move on.

• Keep it as a valid solution.

• Reject it as an extraneous solution.

In the second example, what is the first step to isolate the absolute value?

• Subtract 24 from both sides.

• Multiply both sides by 24.

• Add 24 to both sides.

• Divide both sides by 24.

What is the result of solving the equation |8 - 3x| = 5x + 24 in the negative case?

• x = -2

• x = -16

• x = 2

• x = 16

What does it mean if the absolute value equation equals a negative number?

• There is one solution.

• There is no solution.

• The equation is incorrect.

• There are two solutions.

In the third example, what is the final conclusion when the absolute value equals -2?

• x = 2

• Infinite solutions

• x = -2

• No solution