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If x is an integer, then what is the least possible value of |99−7x| ?
- a)0
- b)1
- c)5
- d)98
- e)107
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If x is an integer, then what is the least possible value of |99&minus...
Case 1: When x is a positive integer
If x is a positive integer, the expression |99 - 7x| can be simplified as 99 - 7x since the absolute value of a positive number is equal to the number itself. In this case, we want to minimize 99 - 7x. The smallest positive integer value for x that still satisfies the given range is x = 14. Plugging this value into the expression, we get |99 - 7(14)| = |99 - 98| = 1.
If x is a positive integer, the expression |99 - 7x| can be simplified as 99 - 7x since the absolute value of a positive number is equal to the number itself. In this case, we want to minimize 99 - 7x. The smallest positive integer value for x that still satisfies the given range is x = 14. Plugging this value into the expression, we get |99 - 7(14)| = |99 - 98| = 1.
Case 2: When x is a negative integer
If x is a negative integer, the expression |99 - 7x| can be simplified as -(99 - 7x) since the absolute value of a negative number is equal to its positive counterpart. In this case, we want to minimize -(99 - 7x) or -99 + 7x. The smallest negative integer value for x that still satisfies the given range is x = -14. Plugging this value into the expression, we get |99 - 7(-14)| = |99 + 98| = 197.
If x is a negative integer, the expression |99 - 7x| can be simplified as -(99 - 7x) since the absolute value of a negative number is equal to its positive counterpart. In this case, we want to minimize -(99 - 7x) or -99 + 7x. The smallest negative integer value for x that still satisfies the given range is x = -14. Plugging this value into the expression, we get |99 - 7(-14)| = |99 + 98| = 197.
Comparing the results from both cases, we see that the smallest possible value of |99 - 7x| is 1. Therefore, the correct answer is B: 1.
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If x is an integer, then what is the least possible value of |99&minus...
The expression |99| is the absolute value of 99. Absolute value is always non-negative, so the least possible value of |99| is 99.
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