Respuesta :
An absolute value inequality is used to represent the situation given that
cases with values above and below the allowance are to be removed.
- The absolute value inequality for the situation is; |x - 125| ≥ 0.25.
Reason:
The given parameter are;
Length of a case x ≤ 125 + 0.25
Length of a case x ≥ 125 - 0.25
Required:
Represent the cases that are to be removed using absolute inequality.
Solution:
The given inequalities sign can be rearranged to give the cases to be
removed as follows;
x ≥ 125 + 0.25
∴ x - 125 ≥ 0.25...(1)
x ≤ 125 - 0.25
x - 125 ≤ -0.25
Multiplying both sides by (-1) gives;
-1×(x - 125) ≥ (-1) × -0.25 = 0.25
-(x - 125) ≥ 0.25...(2)
Therefore;
The given that a case with difference (x - 125) ≥ 0.25 or when (x - 125) is
negative -(x - 125) ≥ 0.25 should be removed, using absolute inequality, we
have;
|x - 125| = (x - 125) when x > 125
|x - 125| = -(x - 125) when x < 125, and (x - 125) is negative
Which gives; A case with length |x - 125| ≥ 0.25 should be removed.
The absolute value inequality that represents the lengths of all the cases
that should removed is therefore;
- |x - 125| ≥ 0.25
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