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Difficulty: EasyIntegers, Absolute Value, and Number Lines

The temperature at the top of a mountain is −14∘C-14^\circ\text{C}, and the temperature at the base of the mountain is 8∘C8^\circ\text{C}. What is the absolute difference, in degrees Celsius, between these two temperatures?

  1. A
    -22
  2. B
    -6
  3. C
    6
  4. D
    14
  5. 22Answer

Answer

22
The correct answer is 22 because the absolute difference between 88 and −14-14 is ∣8−(−14)∣=∣8+14∣=∣22∣=22|8 - (-14)| = |8 + 14| = |22| = 22. This represents the total distance of 22 units between the two temperatures on a number line.

Step-by-Step Solution

1
Translate the problem into a mathematical expression using absolute value for the difference between the two temperatures.
The absolute difference is given by ∣8−(−14)∣|8 - (-14)| or ∣−14−8∣|-14 - 8|.
The absolute difference between two numbers aa and bb on a number line is defined as ∣a−b∣|a - b|.
2
Simplify the subtraction inside the absolute value.
8−(−14)=8+14=228 - (-14) = 8 + 14 = 22 (or −14−8=−22-14 - 8 = -22).
Subtracting a negative number is equivalent to adding its positive counterpart.
3
Evaluate the absolute value.
∣22∣=22|22| = 22 (or ∣−22∣=22|-22| = 22).
The absolute value of a number represents its non-negative distance from zero.

Key Concept

Integers, Absolute Value, and Number Lines
Estimated Time:45s
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Topics

Integers, Absolute Value, and Number Lines

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