Solving Absolute Value Equations

This video tutorial covers the concept of absolute value equations, explaining their definition and how to solve them. It begins with an introduction to the theory behind absolute value equations, followed by basic and advanced examples. The tutorial also addresses special cases where solutions may not exist. Finally, it applies the concept to a real-world problem involving weight limits, demonstrating how to set up and solve an absolute value equation in a practical context.

What is an absolute value equation?

• An equation that always has a single solution

• An equation with only positive numbers

• An equation with no variables

• An equation that includes at least one absolute value expression

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

• 5 and -5

• 5 and -10

• 5 and 0

• 5 and 10

How do you solve an absolute value equation like |x| = 11?

• x = 11 or x = 22

• x = 11 or x = -11

• x = 11 or x = 0

• x = 11 or x = -22

What is the first step in solving the equation |Q + 3| = 6?

• Rewrite as Q + 3 = 6 or Q + 3 = -6

• Rewrite as Q + 3 = 6 or Q + 3 = 0

• Subtract 3 from both sides

• Add 3 to both sides

In the equation 4|y| = 24, what is the value of y?

• 12 or -12

• 4 or -4

• 24 or -24

• 6 or -6

How do you solve the equation |Z - 3| = 4?

• Z = 3 or Z = -3

• Z = 1 or Z = -7

• Z = 4 or Z = -4

• Z = 7 or Z = -1

What is the solution to the equation |x - 5| = 0?

• x = 0

• x = 10

• x = -5

• x = 5

What should you conclude if you get an absolute value equation equal to a negative number?

• The solution is zero

• There is no solution

• There are two solutions

• There is one solution

In the context of the strawberry grower problem, what is the maximum acceptable weight of a case?

• 31.0 pounds

• 30.4 pounds

• 29.6 pounds

• 30.0 pounds

How do you set up an absolute value equation to find the acceptable weight range for the strawberry cases?

• |x - 30| = 0.4

• |30 - x| = 0.4

• |x - 30| = 4

• |30 - x| = 4