Question

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?

Answer 1

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

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:

`\mid x \mid = x, \text{if x} > 0\\~~~~~= -x , \text{if x} < 0`

• Example:

1)
`\mid 3 \mid = 3\\\mid -3 \mid = -(-3) = 3`

2)
`\mid 7 \mid = 7\\\mid -7 \mid = -(-7) = 7`

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