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Jamie told his math teacher: "Give me any absolute value, and I can tell you two numbers that have that absolute value." Is Jamie correct? For any given absolute value, will there always be two numbers that have that absolute value?

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Answer:

Jamie was correct in saying that there could be two numbers who have the same absolute value.

Step-by-step explanation:

  • Absolute value describes or tells us about the distance of a number on the number line from zero and that number without considering which direction from zero the number lies.
  • The absolute value of a number is never negative.
  • We can write the absolute value of a number as:

[tex]\mid x \mid = x, \text{if x} > 0\\~~~~~= -x , \text{if x} < 0[/tex]

  • Example:

1) [tex]\mid 3 \mid = 3\\\mid -3 \mid = -(-3) = 3[/tex]

2) [tex]\mid 7 \mid = 7\\\mid -7 \mid = -(-7) = 7[/tex]

  • Thus, Jamie was correct in saying that there could be two numbers who have the same absolute value.

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