Question

You need to drill a hole in a piece of metal for a machine shop project. The specifications indicate that the diameter of the hole should be at least 0.355 inch and at most 0.375 inch. Write an absolute value inequality that represents the acceptable diameters of the hole.

Answer 1

\[ \large 0.355\leq D\leq0.375 \]

Answer 2

ok for the answer it said that it is [x- 0.365]≤ 0.010
* []=ablsolute value
How did they get that?

Answer 3

sorry i had to for a while:
\[ \large 0.355\leq D\leq0.375 \]
substracting 0.365 u get
\[ \large -0.010\leq D-0.365\leq0.010 \]
from this
\[ \large |D-0.365|\leq0.010 \]

Answer 4

how did you know to subtract 0.365?

Answer 5

that's the only number with which u get the same number (but with different sign) on both extremes.

Answer 6

so what is the equation to find 0.365?

Answer 7

what is the middle point between 0.355 and 0.375

Answer 8

??

Answer 9

oh so you add them both and divide by 2 right so it would = to 0.365

Answer 10

yes

Answer 11

oh ok and how did you isolate the -0.10 & 0.10 to be at the end of the inequality equation?

Answer 12

do you multiply it them?

Answer 13

*do you multiply them ? srry

Answer 14

no i substracted
\[ \large 0.375-0.365=0.010 \]
and
\[ \large 0.355-0.365=-0.010 \]

Answer 15

yea but the final equation is \[| D- 0.365|\le 0.010\] , howd you get from
-0.10<=D-0.365<=0.10?

Answer 16

oh. it is a theorem from calculus (absolute value):
\[ \large |a|\leq b\Leftrightarrow\begin{cases}
b\geq0\\
\text{and}\\
-b\leq a\leq b
\end{cases} \]

Answer 17

oh well i haven't learned that yet, that's why i didn't know

Answer 18

well. now u know :)

Answer 19

Well i know how it looks like but, not how it works .

Answer 20

Ill just wait till class so the teacher can explain because it looks to complicated for you to explain through here. So thanks for the help!

Answer 21

u r welcome