Solving One-Variable Absolute Value Equations

The video tutorial covers absolute value equations, explaining what they are and how to solve them. It begins with a definition and examples, then discusses what constitutes a valid solution. The tutorial provides step-by-step instructions for solving these equations, including handling special cases where no solution exists.

What is a necessary component of an absolute value equation?

• An equal sign and no variables

• An equal sign and at least one variable inside the absolute value

• No equal sign but at least one variable inside the absolute value

• Only numbers inside the absolute value

Which of the following is NOT an absolute value equation?

• |x| = 7

• |x - 3| = 5

• |2x + 1| = x + 4

• x + |-4| = 21 - 2x

What does it mean for a value to be a solution to an equation?

• It makes the equation complex

• It makes the equation undefined

• It makes the equation true

• It makes the equation false

If the absolute value of x is equal to 7, what are the possible values of x?

• 7 and 0

• Only -7

• Only 7

• 7 and -7

What is the solution to the equation |2x - 1| = 5?

• x = -3 or x = -2

• x = 3 or x = -2

• x = -3 or x = 2

• x = 3 or x = 2

In the equation 3| -x + 2 | - 1 = 8, what is the first step to isolate the absolute value?

• Divide by 3

• Subtract 1 from both sides

• Multiply by 3

• Add 1 to both sides

What are the solutions to the equation | -x + 2 | = 3?

• x = 1 or x = -5

• x = -1 or x = -5

• x = -1 or x = 5

• x = 1 or x = 5

What is the solution to the equation 1/3 | 5 - 25x | = 15?

• x = -8/5 or x = 2

• x = 8/5 or x = -2

• x = -8/5 or x = -2

• x = 8/5 or x = 2

What is the solution to the equation -|12x + 7| / 9 = 0?

• x = 0

• x = 7/12

• No solution

• x = -7/12

Why does the equation -2| -x + 1 | = 14 have no solution?

• Because the equation is complex

• Because the equation is undefined

• Because x cannot be negative

• Because absolute value cannot be negative