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Difficulty: EasyOrder of Operations and Number Properties

What is the value of the expression ∣−8∣−∣6−11∣|-8| - |6 - 11|?

  1. A
    -13
  2. B
    -9
  3. C
    -3
  4. 3Answer
  5. E
    13

Answer

3
To find the value of the expression, first simplify the expression inside the absolute value bars: 6−11=−56 - 11 = -5. Next, apply the definition of absolute value, which makes any value non-negative: ∣−8∣=8|-8| = 8 and ∣−5∣=5|-5| = 5. Finally, subtract the two values: 8−5=38 - 5 = 3.

Step-by-Step Solution

1
Evaluate the subtraction inside the second absolute value grouping.
6−11=−56 - 11 = -5
Operations inside grouping symbols, such as parentheses or absolute value bars, must be performed first.
2
Apply the absolute value operation to both terms.
∣−8∣=8|-8| = 8 and ∣−5∣=5|-5| = 5
The absolute value of a number is its distance from zero, which is always non-negative.
3
Substitute the evaluated absolute values back into the expression and subtract.
8−5=38 - 5 = 3
Complete the final subtraction operation as indicated by the expression.

Key Concept

Absolute value acts as a grouping symbol in the order of operations, and the absolute value of any real number is non-negative.
Estimated Time:45s
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Topics

Order of Operations and Number Properties

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