Question

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the width of a machine part should be 1.25 centimeters (cm). the manufacturing tolerance is within 0.04 cm. the equation |x - 1.25| = 0.04 models this context.
what is the minimum width of the machine part, in centimeters?

Explanation:

Step1: Understand absolute value equation

The equation \(|x - 1.25| = 0.04\) means \(x - 1.25 = 0.04\) or \(x - 1.25=- 0.04\) (by the definition of absolute value: \(|a| = b\) implies \(a = b\) or \(a=-b\) for \(b\geq0\)).

Step2: Solve for minimum width

To find the minimum width, we consider the case where \(x - 1.25=-0.04\) (since we want the smaller value of \(x\)).
Solve \(x - 1.25=-0.04\) for \(x\):
Add \(1.25\) to both sides of the equation: \(x=- 0.04 + 1.25\).
Calculate the right - hand side: \(x = 1.21\).

Answer:

The minimum width of the machine part is \(1.21\) centimeters.