Exploring Absolute Value Equations

The video tutorial explains the concept of absolute value as the distance from zero, always measured as a positive number. It provides examples using a number line to illustrate how absolute values work for both positive and negative numbers. The tutorial then delves into solving absolute value equations, demonstrating how to set up and solve these equations, including more complex examples. It also covers scenarios where absolute value equations have no solution, emphasizing that distance cannot be negative.

What does the absolute value of a number represent?

• The distance from zero

• The square of the number

• The number itself

• The negative of the number

How is the absolute value of -5 calculated?

• By counting 5 units to the right of zero

• By counting 5 units to the left of zero

• By taking the negative of -5

• By adding 5 to zero

What is the absolute value of 7?

• 7

• 14

• 0

• -7

If the absolute value of x is 5, what are the possible values of x?

• 0 and -5

• 5 and 10

• 5 and 0

• 5 and -5

Which two values are 8 units away from zero?

• 0 and -8

• 8 and 16

• 8 and 0

• 8 and -8

What should you do if an absolute value equation equals a negative number?

• Ignore the negative sign

• State that there is no solution

• Solve for the negative value

• Solve for the positive value

In the equation |x + 4| = 10, what are the possible values of x?

• 4 and -4

• 6 and -14

• 14 and -6

• 10 and -10

For the equation |2c - 2| = 6, what are the solutions for c?

• 4 and -2

• 3 and -3

• 2 and -4

• 6 and -6

What is the solution to the equation |t + 2| = 5.5?

• 3.5 and -7.5

• 2.5 and -2.5

• 5.5 and -5.5

• 7.5 and -3.5

Why does the equation |x + 5| = -4 have no solution?

• Because x cannot be positive

• Because absolute value cannot be negative

• Because x cannot be negative

• Because the equation is not valid