For 1 <= x <= 2 the expression |x - 1| + |x - 2| is equivalent to which of the following?

Rationale

For 1 <= x <= 2, the expression |x - 1| + |x - 2| simplifies to 1.

Within the interval [1, 2], the absolute values can be evaluated directly. Specifically, |x - 1| equals (x - 1) and |x - 2| equals (2 - x), leading to the simplified expression of 1.

A (3-2x) YOUR ANSWER

This expression represents a linear function that decreases as x increases. Substituting values from the interval [1, 2] yields results that do not consistently equal 1, demonstrating that this option does not match the original expression.

B (2x-3) YOUR ANSWER

While this expression is also linear, substituting x = 1 and x = 2 gives results of -1 and 1, respectively. Thus, it does not hold true for the entire interval [1, 2], making it an incorrect choice.

C (2x + 3) YOUR ANSWER

This expression increases as x increases and yields values of 5 and 7 for x = 1 and x = 2, respectively. This significant deviation from the constant value of 1 shows it does not represent the original expression over the specified interval.

D (1) CORRECT

During the evaluation of the original expression |x - 1| + |x - 2| within the interval [1, 2], we find that it consistently results in 1, confirming this choice as correct.

Conclusion

The expression |x - 1| + |x - 2| evaluates to 1 for all x values in the range [1, 2]. This conclusion is supported by direct evaluation of the absolute values within the specified interval. The other choices provide varying linear results that do not coincide with the constant outcome of 1, clearly establishing choice D as the accurate answer.

For 1 <= x <= 2 the expression |x - 1| + |x - 2| is equivalent to which of the following?

For 1 <= x <= 2, the expression |x - 1| + |x - 2| simplifies to 1.

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