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Answer :
The absolute value of inequality representing the range of John's weight is | x - 156 | ≤ 8.
What is absolute value of inequality?
An absolute value inequality is an inequality that contains an absolute value expression. The absolute value of a number represents the distance between that number and zero on a number line.
What is absolute value expression?
An absolute value expression is a mathematical expression that contains an absolute value function, denoted by vertical bars around a number or expression. The absolute value of a number is its distance from zero on a number line, so an absolute value expression represents a positive number, regardless of whether the original number was positive or negative.
As per the given question,
If John weighed 156 pounds give or take 8 pounds ten years ago, then his weight could have been anywhere from 156 - 8 = 148 pounds to 156 + 8 = 164 pounds.
To write this as an absolute value inequality, we can let x represent John's weight, and use the absolute value to represent the distance from the mean weight of 156 pounds. The inequality would be:
| x - 156 | ≤ 8
This inequality says that the distance between John's weight (x) and the mean weight of 156 pounds must be less than or equal to 8 pounds. In other words, John's weight must be within 8 pounds of 156, which represents the range of possible weights he could have had ten years ago.
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