A bearing for a new sports car must be manufactured within 0.001 mm of its circumference of 2.35 mm. Write and solve an absolute value inequality to describe the largest and the smallest possible circumference for the bearing.

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- Mathhelp346

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- TuringTest

how about if I wrote this:
'the distance between the actual size of the bearing and the perfect size of the bearing must be no more than x'
?
that is very similar to the last statement you had

- Mathhelp346

?

- TuringTest

let the actual size be b
let the optimal size be a
let the limit of error be x
'the distance between a and b must be no more than x'
can you write that as you did the other?
what are a and x ?

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## More answers

- Mathhelp346

is a 0.001 and b 2.35

- TuringTest

I called the limit of error x, so x=0.001
a would be the optimal measurement
the actual measurement 'b' will be the variable
'A bearing for a new sports car must be manufactured within 0.001 mm of its circumference of 2.35 mm'
=
'the distance between a and b must be no more than x'
'no more than' means 'less-than or equal-to', so we have
\[|a-b|\le x\]\[|2.53-b|\le 0.001\]solve for b

- TuringTest

typo above*\[|2.35-b|=0.001\]

- Mathhelp346

? why is it =?

- Mathhelp346

shouldnt it be <

- TuringTest

sorry another typo!

- Mathhelp346

lol

- TuringTest

\[|2.35-b|\le0.001\]or maybe\[|2.35-b|<0.001\]not really clear...

- Mathhelp346

why is 0.001 there?

- TuringTest

that is the maximum error in measurement
like I said it is like saying
'the distance between the actual measurement and the optimal measurement (2.35) must be no more than 0.001'
treat these as points on a number line as before:\[|2.35-b|\le0.001\]

- Mathhelp346

oh ok i get it

- TuringTest

|dw:1328239501252:dw|

- Mathhelp346

ok

- TuringTest

b can be any point on that shaded part|dw:1328239612650:dw|so we can write\[|a-b|\le x\]

- Mathhelp346

ok

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