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Question

Difficulty: EasyProperties of Integers

What is the value of the expression −3×∣−2∣−(−5)-3 \times |-2| - (-5)?

  1. -1Answer
  2. B
    11
  3. C
    -21
  4. D
    -11

Answer

The correct answer is -1.
The expression must be solved by first finding the absolute value of −2-2, which is 22. Multiplying −3-3 by 22 gives −6-6. Finally, subtracting −5-5 from −6-6 is the exact same as adding 55 to −6-6, which results in −1-1.

Step-by-Step Solution

1
Evaluate the absolute value expression.
∣−2∣=2|-2| = 2
Absolute value represents the distance of a number from zero, which is always non-negative.
2
Perform the multiplication.
−3×2=−6-3 \times 2 = -6
According to the order of operations (PEMDAS), multiplication must be completed before addition and subtraction. Multiplying a negative integer by a positive integer yields a negative integer.
3
Perform the subtraction.
−6−(−5)=−6+5=−1-6 - (-5) = -6 + 5 = -1
Subtracting a negative integer is mathematically equivalent to adding its positive counterpart.

Key Concept

Integer Sign Rules and Order of Operations
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Topics

Properties of Integers

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