Understanding Absolute Value Equations

The video tutorial explains how to solve absolute value equations by providing two examples. The first example involves finding solutions for the equation |x| = 4, which results in x = -4 and x = 4. The second example involves solving |x + 4| = 12, leading to solutions x = 8 and x = -16. The tutorial emphasizes the importance of isolating the absolute value and setting up two equations to find solutions. It also highlights the need to verify solutions by substituting them back into the original equation. The video concludes with a promise of more examples in the next video.

What is the absolute value of a number?

• The number itself

• The negative of the number

• The square of the number

• The distance of the number from zero

How many solutions does the equation |x| = 4 have?

• One solution

• Two solutions

• Three solutions

• No solution

Which numbers have an absolute value of 4?

• Neither 4 nor -4

• Both 4 and -4

• Only -4

• Only 4

What is the first step in solving the equation |x + 4| = 12?

• Set up two separate equations

• Subtract 4 from both sides

• Add 4 to both sides

• Multiply both sides by 4

What are the solutions to the equation |x + 4| = 12?

• x = 4 and x = -4

• x = 16 and x = -8

• x = 12 and x = -12

• x = 8 and x = -16

In the equation |x + 4| = 12, what does setting up two equations involve?

• Dividing both sides by 4

• Multiplying both sides by 12

• Setting x + 4 equal to 12 and -12

• Adding 4 to both sides

What is the general strategy for solving absolute value equations?

• Multiply the absolute value by the variable

• Add the absolute value to both sides

• Isolate the variable

• Isolate the absolute value and solve two equations

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

• To ensure the solutions are positive

• To verify the solutions satisfy the original equation

• To find additional solutions

• To simplify the equation further

What is the absolute value of -12?

• 0

• 12

• 24

• -12

What should you do after solving an absolute value equation?

• Check the solutions in the original equation

• Add the solutions together

• Multiply the solutions by 2

• Ignore the solutions