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Question

Difficulty: EasyIntegers, Absolute Value, and Number Lines

If x=−6x = -6, what is the value of the expression 12−∣x−3∣12 - |x - 3|?

Answer: 3

Answer

The value of the expression is 3.
Substituting x=−6x = -6 into the expression 12−∣x−3∣12 - |x - 3| gives 12−∣−6−3∣12 - |-6 - 3|. Simplifying the subtraction inside the absolute value gives 12−∣−9∣12 - |-9|. Since the absolute value of −9-9 is 99, the expression simplifies to 12−912 - 9, which equals 33.

Step-by-Step Solution

1
Substitute x=−6x = -6 into the expression.
12−∣−6−3∣12 - |-6 - 3|
Substitute the given value of the variable into the algebraic expression.
2
Simplify the expression inside the absolute value symbol.
12−∣−9∣12 - |-9|
Subtracting 3 from −6-6 results in −9-9.
3
Calculate the absolute value.
12−912 - 9
The absolute value represents the distance from zero on the number line, so ∣−9∣=9|-9| = 9.
4
Subtract the numbers to find the final value.
33
12−9=312 - 9 = 3.

Key Concept

Evaluating algebraic expressions involving integers and absolute values.
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Topics

Integers, Absolute Value, and Number Lines

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