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Question

Difficulty: EasyAbsolute Value

What is the value of the expression 12−2∣−4+1∣12 - 2|-4 + 1|?

  1. 6Answer
  2. B
    18
  3. C
    30
  4. D
    2

Answer

6
The expression is evaluated by first simplifying the terms inside the absolute value to get |-3|, which equals positive 3. Multiplying this by the coefficient 2 gives 6. Finally, subtracting 6 from 12 yields the correct answer of 6.

Step-by-Step Solution

1
Simplify the expression inside the absolute value bars.
−4+1=−3-4 + 1 = -3
According to the order of operations, operations inside absolute value bars (which act as grouping symbols) must be performed first.
2
Evaluate the absolute value of the result.
∣−3∣=3|-3| = 3
The absolute value of a number represents its distance from zero, which is always positive.
3
Multiply the result by the coefficient outside the absolute value.
2×3=62 \times 3 = 6
Multiplication must be performed before subtraction according to the order of operations (PEMDAS).
4
Subtract the product from the initial value.
12−6=612 - 6 = 6
This completes the evaluation of the expression to find the final numerical value.

Key Concept

Absolute Value and Order of Operations
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Topics

Absolute Value

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