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Question

Difficulty: EasyIntegers, Absolute Value, and Number Lines

What is the value of the expression ∣−12∣−∣7−15∣|-12| - |7 - 15|?

Answer: 4

Answer

The value of the expression is 4.
The absolute value of a number represents its distance from zero on a number line, so ∣−12∣=12|-12| = 12. Simplifying inside the second term gives 7−15=−87 - 15 = -8, and the absolute value ∣−8∣=8|-8| = 8. Subtracting these two results yields 12−8=412 - 8 = 4.

Step-by-Step Solution

1
Evaluate the first term
∣−12∣=12|-12| = 12
The absolute value of a number is its distance from zero on the number line, which is always non-negative.
2
Simplify the expression inside the second absolute value
7−15=−87 - 15 = -8
Subtracting 15 from 7 yields a negative difference of -8.
3
Evaluate the second absolute value term
∣−8∣=8|-8| = 8
The absolute value of -8 is 8.
4
Subtract the two evaluated terms
12−8=412 - 8 = 4
Subtracting 8 from 12 gives the final simplified value of 4.

Key Concept

Evaluating expressions with absolute values requires simplifying the terms inside the absolute value grouping symbols first, taking the absolute value of the result, and then performing the subtraction.
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Topics

Integers, Absolute Value, and Number Lines

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