Question

4. A quality control inspector is in charge of inspecting drill bits that are produced on an assembly line. The diameter of a drill bit can be modeled by the equation |x − 0.525| = 0.01. Show your work in solving the equation to determine the minimum and maximum diameters of the drill bits.

Answer 1

Please help I don't understand

Answer 2

0.01 is the accepted tolerance for the drill bit

Answer 3

There's supposed to be two answers to the equation.

Answer 4

if there is a tolerance that means the drill bit can be
-slightly above or
-slightly below

the specified diameter.

Answer 5

The first equation is x - 0.0525 = 0.01. The 2nd is: x - 0.0525 = -0.01

Answer 6

Okay.

Answer 7

Is the answer to the first one 0.0625?

Answer 8

0.0625 - 0.0525 = 0.1, right?

Answer 9

Right, and the answers to both of those equations will equal the minimum and maximum diameters of the drill bits.

Answer 10

yes

Answer 11

the second diameter (minimum diameter) gives a negative number in the absolute bracket, and the absolute again gives the required 0.1

Answer 12

Yes

Answer 13

so the second one is x=0.0425

0.0425 - 0.0525 = -0.01, |-0.01|=0.01

Answer 14

like already stated above

Answer 15

So the answer to the second one is 0.0425, correct?

Answer 16

correct

Answer 17

minimum diameter is 0.0425

Answer 18

So the minimum diameter of the drill bits is 0.425. And the maximum is 0.625.

Answer 19

yes

Answer 20

both have a deviation of no more than 0.01

Answer 21

Thanks a lot.

Answer 22

no problem

Answer 23

Could you help me on another? But slightly different?

Answer 24

OK

Answer 25

Max was solving the equation below and isn’t sure if his answer is correct. Explain to Max how he can check his answer and then help him identify any errors he made. Provide the correct solution in your explanation.

3x + 6/8 = 7x – 1/6
24/1(3x + 6/8) = 24/1(7x – 1/6)

3(3x + 6) = 4(7x – 1)
9x + 18 = 28x – 1)
9x – 9x + 18 = 28x – 9x – 1
18 = 19x – 1
18 + 1 = 19x – 1 + 1
19 = 19x
1 = x

Answer 26

@mathessentials

Answer 27

he could substitute the x in the original equation..

Answer 28

I figured it out on my own but I seemed to have gotten it wrong too

Answer 29

Here's my "revised" version:

The mistake he made was on Line #5. When he multiplied 4 x 7x he didn’t multiply 4 x 1 which was also in the parenthesis. Here’s my solution:

3x + 6/8 = 7x – 1/6
24/1(3x + 6/8) = 24/1(7x – 1/6)

3(3x + 6) = 4(7x – 1)
9x + 18 = 28x – 4
9x – 9x + 18 = 28x – 9x – 4
18 = 19x – 4
18 + 4 = 19x – 4 + 4
22 = 19x
1.2 ≈ x

Answer 30

But I checked my answer and it's not right.

Answer 31

the fist difference is in the line

9x – 9x + 18 = 28x – 9x – 4

Answer 32

no

Answer 33

one before actually

Answer 34

That's what I said.

Answer 35

yes, max did not multiply the second part of the paranthesis

Answer 36

He did do 4 x 7x but didn't do 4 x 1...

Answer 37

exactly

Answer 38

Yes, but what did I do wrong? ANd did Max do anything else wrong before or after that?

Answer 39

3x + 6/8 = 7x – 1/6
24/1(3x + 6/8) = 24/1(7x – 1/6)

what did he try to do there?

Answer 40

I'm not sure I don't know where he got the "24/1" from

Answer 41

yeah.... thats hard to understand

Answer 42

This is what the equation originally looked like:

Answer 43

I had to copy & paste it into a Word Document.

Answer 44

thanks

Answer 45

Np just need to get this done

Answer 46

the denominators in the brackets are 6x8, which = 48,
probably has something to do with the 24

Answer 47

he tries to get the same common denominator

Answer 48

Oh yeah he broke 48 down...

Answer 49

what he should have done
\[\frac{ 6 \times (3x+6) }{6 \times 8 }=\frac{ 8 \times (7x-1) }{8 \times 6 }\]

Answer 50

Oh he should have multiplied the denominators?

Answer 51

Its clear

Answer 52

he should get the same denominators by multiplying the one with the other and
multiplying the numerator with the "foreign" denominator

because you're allowed to multiply by any fraction that makes one, like
8/8 or 7/7 or 6/6, when you multiply with a number down must also with the same one up

Answer 53

So could you figure out the problem? And walk me through it?

Answer 54

\[\frac{ 1 }{ 3 } + \frac{ 2 }{ 5 } =\frac{ 5 \times 1 }{ 5 \times 3 } + \frac{ 3 \times 2 }{ 3 \times5 }\]

Answer 55

Where did you get those fractions from?

Answer 56

they are example!!

Answer 57

Ohhhhhh

Answer 58

on how to get a common denominator
it's the same principle in the equation

Answer 59

Modulus is given so for min. answer modulus will be negative i.e., |x − 0.0525| will be --(x-0.0525) and for max it will be +(x-0.0525) then solve to get the the value of x in each case

Answer 60

So is this what I have so far?
\[\frac{ 3x + 6 }{ 40 } = \frac{ 7x - 1 }{ 40 }\]

Answer 61

8x6 is 48

Answer 62

@Addu5221 we're on a different question.

Answer 63

My bad...

Answer 64

ohk sorry

Answer 65

and also you must do the operations on both parts of the fraction
so also make 6(3x + 4)

Answer 66

3x+6*

Answer 67

the fraction itself should not be changed in value
so if multiply below
must multiply above

Answer 68

This is what we have so far right?
\[\frac{ 3x + 6 }{ 48 } = \frac{ 7x - 1 }{ 48 }\]

Answer 69

\[\frac{ 6 \times (3x+6) }{ 48 }=\frac{ 8 \times (7x-1) }{ 48 }\]

Answer 70

Oh, okay so we have to do: 6 x 3x + 6 = 8 x 7x - 1?

Answer 71

yes see above

Answer 72

Hold on let me type this out on my Word Document

Answer 73

But revised version is perfect

Answer 74

if you changed only the denominator, and the numerator is the same
then:

both (x + ) terms are divided by the same number, which is not what
the problem stated. they have different fractions and
if we want them to have the same fractions we must compensate that

Answer 75

Okay, I'm back.

Answer 76

what is this discussion for greenlegodude your revise version is correct

Answer 77

@Addu5221
This is the question we are working on:

Max was solving the equation below and isn’t sure if his answer is correct. Explain to Max how he can check his answer and then help him identify any errors he made. Provide the correct solution in your explanation.

3x + 6/8 = 7x – 1/6
24/1(3x + 6/8) = 24/1(7x – 1/6)

3(3x + 6) = 4(7x – 1)
9x + 18 = 28x – 1)
9x – 9x + 18 = 28x – 9x – 1
18 = 19x – 1
18 + 1 = 19x – 1 + 1
19 = 19x
1 = x

Answer 78

Yes I get that Mathessentials

Answer 79

good :)

Answer 80

so where are we at

Answer 81

So 6 x 3x + 6. We solve this first. So: subtract 6 from both sides?

Answer 82

@Addu5221

Here is the exact mistake Max made:

Answer 83

So 6 x 3x + 6. We solve this first. So: subtract 6 from both sides?

So then we have 0 x 3x? I don't get it....

Answer 84

"6 x 3x + 6."

where from?

Answer 85

Um, that's from the numerator of the first fraction.

Answer 86

I see

Answer 87

OK so what max did was this: he found the smallest number that is divisible
by 8 and by 6

Answer 88

Since we multiplied 6 to the denominator of the 1st fraction. So we have to do it to the numerator, correct?

Answer 89

RIght

Answer 90

yes the numerator would be 48

Answer 91

You mean the denominator right?

Answer 92

you can always get a common denominator by multiplying the different ones together
however there's also a smaller multiplication sometimes that gives the same result

Answer 93

you are right, the denominator

Answer 94

e.g. 8 and 6
48 is a common one

however 24 also is (3 and 4)

Answer 95

max chose the smallest possible whihc is 24 instead of 48
that is not an error

Answer 96

the first error he did was by skipping 4x -1

Answer 97

Yes I know about getting a common denominator like say if youi have 1/2 and 3/4 the common denominator is 4 because 2 x 2 = 4 and 4 x 1 = 4. It's not 8 because there is a smaller number that can go into both of these.