   Chapter 1.2, Problem 92E

Chapter
Section
Textbook Problem

Quality Control The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality|x − 0.1| < 0.01What is the smallest diameter a ball bearing in the batch can have? The largest diameter?

To determine
The smallest and largest diameter of given ball bearing.

Explanation

Given:

The diameter of the ball bearing is x inch and the inequality satisfies the manufacturing criteria is |x1|0.01

Calculation:

The absolute value of a number a is denoted by |a| and is defined as,

|a|={aifa0aifa<0

Expand the absolute value function from the definition of absolute value. The equations becomes,

|x0.1|={(x0.1)if(x0.1)0(x0.1)if(x0.1)<0

For (x0.1)0 , the expression becomes,

(x0

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