Solving Absolute Value Equations

This video tutorial covers the concept of absolute value, explaining it as the distance from zero on a number line. It defines absolute value mathematically and demonstrates how to solve absolute value equations by splitting them into two cases: when the quantity inside is positive and when it is negative. The video also addresses more complex problems and emphasizes the importance of checking solutions against the original equation. Finally, it provides a recap and encourages practice.

What does the absolute value of a number represent?

• The negative of the number

• The distance from zero on the number line

• The number itself

• The square of the number

What is the absolute value of -4?

• 0

• 8

• 4

• -4

How can we mathematically convert a negative number to a positive number?

• By adding 1

• By taking its opposite

• By subtracting 1

• By multiplying by 2

What is the absolute value of a if a is greater than or equal to zero?

• a

• -a

• 0

• 1

What is the absolute value of a if a is less than zero?

• 1

• 0

• -a

• a

When solving the equation |x - 7| = 2, what are the two possible equations?

• x - 7 = 2 and x - 7 = -2

• x - 7 = 2 and x + 7 = 2

• x - 7 = 2 and x - 7 = 0

• x + 7 = 2 and x + 7 = -2

What are the solutions to the equation |x - 7| = 2?

• x = 5 and x = 9

• x = 5 and x = -9

• x = -5 and x = 9

• x = -5 and x = -9

Why is it important to check solutions in the original equation?

• To ensure the solutions are correct

• To find more solutions

• To simplify the equation

• To change the equation

What should you do first when solving a more complex absolute value equation?

• Subtract 1 from both sides

• Multiply by 2

• Add 1 to both sides

• Isolate the absolute value

What are the two types of equations you split an absolute value equation into?

• Positive and zero

• Positive and negative

• Negative and zero

• Zero and one