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Question

Difficulty: EasyAbsolute Value

What is the value of the following expression?

∣−4−∣−9∣∣|-4 - |-9||

Answer: 13

Answer

13
The correct answer is found by first evaluating the innermost absolute value, ∣−9∣=9|-9| = 9. Substituting this value back into the expression gives ∣−4−9∣|-4 - 9|. Simplifying the subtraction inside yields ∣−13∣|-13|. Finally, the absolute value of −13-13 is 1313.

Step-by-Step Solution

1
Evaluate the inner absolute value.
∣−9∣=9|-9| = 9
According to the order of operations, we must simplify the expression from the inside out. The absolute value of a negative number is its positive counterpart.
2
Substitute and simplify the remaining expression.
∣−4−9∣=∣−13∣|-4 - 9| = |-13|
Replacing ∣−9∣|-9| with 99 gives the subtraction −4−9-4 - 9, which simplifies to −13-13.
3
Evaluate the outer absolute value.
∣−13∣=13|-13| = 13
The absolute value represents the distance from zero on the number line, which is always non-negative.

Key Concept

Absolute Value
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Topics

Absolute Value

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