Exploring Absolute Value Equations

The video tutorial covers absolute value equations, starting with an introduction to the concept of absolute value as the distance from zero. It explains that absolute value equations can have two solutions and provides steps to solve them. The tutorial includes examples, highlights common mistakes, and discusses properties of absolute values. It concludes with practice problems and solutions, emphasizing the importance of isolating the absolute value before solving.

What is the absolute value of -5?

• -5

• 0

• 5

• 10

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

• -5 and 0

• 5 and 10

• 0 and 5

• 5 and -5

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

• Multiply by 3

• Isolate the absolute value

• Add 7 to both sides

• Rewrite as two cases

In the equation |x + 7| = 8, what are the two cases to consider?

• x + 7 = 0 and x - 7 = 0

• x - 7 = 8 and x - 7 = -8

• x + 7 = 8 and x - 7 = 8

• x + 7 = 8 and x + 7 = -8

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

• Solve for x

• Isolate the absolute value

• Rewrite as two cases

• State that there are no solutions

If |x| = 0, how many solutions does the equation have?

• One

• Infinite

• None

• Two

What is the absolute value equation for inline skate wheels with a diameter of 7.4 mm and a variance of 0.1 mm?

• |x + 7.4| = 0.1

• |x + 0.1| = 7.4

• |x - 7.4| = 0.1

• |x - 0.1| = 7.4

How do you find the midpoint when creating an absolute value equation from two numbers?

• Divide the larger number by the smaller number

• Multiply the numbers

• Subtract the smaller number from the larger number

• Add the numbers and divide by 2

In the equation |y + 2| = 8, what are the solutions for y?

• 6 and -10

• 8 and -8

• 2 and -2

• 10 and -6

What is the solution to the equation |d/3| = 3?

• d = 6 and d = -6

• d = 9 and d = -9

• d = 1 and d = -1

• d = 3 and d = -3