Solving Absolute Value Equations Challenge

What does the absolute value of a number represent?

• The square of the number

• The negative of the number

• The distance between the number and zero on a number line

• The number itself

If the absolute value of a is 4, what are the possible values of a?

• 4 and -4

• 4 and 0

• Only 4

• Only -4

In the equation |x - 3| = 8, what are the two possible values of x?

• 11 and -5

• 8 and -8

• 3 and -3

• 5 and -11

Why is it important to check your solutions after solving an absolute value equation?

• To ensure the solutions are positive

• To verify that the solutions satisfy the original equation

• To find additional solutions

• To simplify the solutions

In the equation |2x - 7| - 5 = 4, what is the first step to isolate the absolute value?

• Divide both sides by 2

• Multiply both sides by 2

• Add 5 to both sides

• Subtract 5 from both sides

What are the solutions to the equation |2x - 7| = 9?

• x = 6 and x = -3

• x = 8 and x = -1

• x = 7 and x = -2

• x = 9 and x = -9

In the equation 2|4 - 5x| - 8 = 6, what is the first step to isolate the absolute value?

• Add 8 to both sides

• Divide both sides by 2

• Subtract 8 from both sides

• Multiply both sides by 2

What are the solutions to the equation |4 - 5x| = 3?

• x = 3/5 and x = 5/5

• x = 2/5 and x = 6/5

• x = 1/5 and x = 7/5

• x = 4/5 and x = 8/5

What should you conclude if the absolute value of an expression equals a negative number?

• The solution is zero

• There is no solution

• There is one solution

• There are two solutions

Why can't the absolute value of an expression be negative?

• Because it is always positive or negative

• Because it is always zero

• Because it represents the square of the number

• Because absolute value represents distance, which cannot be negative