Solving Absolute Value Equations Step-by-Step

This video tutorial covers solving absolute value equations, starting with a review of absolute value as the distance from zero. The instructor demonstrates how to isolate the absolute value in equations and solve them by splitting into two cases: positive and negative. Examples are provided, including a trick question with no solution. The tutorial also includes practice problems and a word problem involving absolute deviation, emphasizing the importance of checking solutions and understanding the concept of deviation in real-world contexts.

What does the absolute value of a number represent?

• The number itself

• The distance from zero

• The negative of the number

• The square of the number

If the absolute value of a number is 4, what could the original number be?

• 4 or 8

• 4 or -2

• 4 or 0

• 4 or -4

What is the first step in solving an absolute value equation?

• Add a constant to both sides

• Isolate the absolute value quantity

• Multiply both sides by a constant

• Square both sides

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

• 4 and 0

• 8 and 0

• 4 and -4

• 8 and -4

Why does the equation |2x - 3| = -2 have no solution?

• Because x cannot be a fraction

• Because 2x - 3 is always positive

• Because absolute value cannot be negative

• Because 2x - 3 cannot be negative

How do you solve the equation |x + 5| = 3?

• By adding 5 to both sides

• By splitting it into x + 5 = 3 and x + 5 = -3

• By multiplying both sides by 3

• By subtracting 5 from both sides

What are the solutions to the equation |x + 5| = 3?

• x = 3 or x = -3

• x = -2 or x = -3

• x = 2 or x = -2

• x = -2 or x = -8

In the equation |x - 4| = 9, what are the possible values of x?

• 4 and -4

• 9 and -9

• 13 and 5

• 13 and -5

What is the absolute deviation in the basketball hoop problem?

• 0.5 inches

• 0.25 inches

• 1 inch

• 2 inches

What is the maximum height the basketball hoop can be set at?

• 120 inches

• 119.75 inches

• 120.25 inches

• 121 inches