Question

Solve the equation |27-75x|=-1000 .

Answer 1

i think i just have to solve each the negative and positive one right?

Answer 2

yes/

Answer 3

Is there ANY number y such that |y| = -1?

Or such that |y| = -1000?

Answer 4

thanks!

Answer 5

No; look at what I'm saying.

Answer 6

what do you mean?

Answer 7

Your problem has this expression:
|27-75x|=-1000

But can there be any number y such that |y| = -1000?

No, there can't because |y| is always positive or zero. |y| can never have a negative value.

So |27-75x|=-1000 is meaningless.

Answer 8

Hence the equation |27-75x|=-1000
has NO solutions.

Answer 9

when i was told to find this answer i was told to get 2 answers one negative and one positive

Answer 10

James is right, ignore FoolforMath.

Answer 11

That works for | something | = a positive number or zero

but if | something | = negative number,
then the expression is inconsistent/meaningless/invalid and has no solutions.

Answer 12

@TuringTest: I assumed it's a inequality as the OP is mentioning for solving from both sides.

However,things can be made pretty clear only if you define abs value,

Absolute value of a number is its distance from zero on the number line. The absolute value of a number n is denoted by, |n|.

So,asking for solving |27-75x|=-1000 . is meaningless and insane and stupid ... so I OP meant an inequality instead of equality.

Answer 13

OH i never knew that... so since 1000 is negative that makes the equation no solution?

Answer 14

If you're not convinced, let me ask you: what number y has the property that

| y | = -1000?

Well y = 1000 doesn't work because | 1000 | = 1000

and y = -1000 doesn't work either because | -1000 | = 1000.


So yes, the equation as posed has no solutions.

Answer 15

@MoreForJoe: First learn the definition and then solve the problem :)

Answer 16

i just never knew about the negative part. our professor just threw us a curve-ball

Answer 17

and by number JamesJ means real numbers only,absolute value of complex numbers is a simmilar concept but computation is a bit different ...:)

Answer 18

@MoreForJoe: Let me remind you the definition again ...

*Absolute value of a number is its distance from zero on the number line.*

Distance being a scalar quantity, how can it be negative ? ;)

Answer 19

like James said\[\left| y \right|=-x\]is IMPOSSIBLE because of the concept of the absolute value.
@FoolforMath, if this was an inequality it would still have no solutions\[\left| y \right|\le-x\]cannot be broken into\[-x \le y \le x\]for the same reasons as the equality cannot. think about why

Answer 20

ahhhh ok

Answer 21

JamesJ didn't mentioned the definition anywhere and mostly explained on examples ... oh yes I can see that how can a distance be less than or equal to a negative number ? :O

but well

\[ \left| y \right|\ge-x \]
would have and so do

\[ \left| y \right|\le-x \]

with x=-z,where \[ x,y,z \in \mathbb{R} \] ;)

Answer 22

That's a little far-fetched reasoning don't you think?

Answer 23

Fine. By definition
\[ |x| = \left\{ \begin{matrix}x & \text{ if x > 0} \\ 0 & \text{ if x = 0} \\ -x & \text{ if x < 0}\end{matrix} \right. \]

Hence
if x > 0, then |x| = x > 0
if x = 0, then |x| = 0
if x < 0, then |x| = -x > 0

Therefore
\[|x| \geq 0\]
for all values of x.

Answer 24

@TuringTest:Well,on second thought,may be not as you asked me that question and want me to think over it.

Answer 25

Therefore, for any negative number a, there are no real numbers x such that
\[ |x| = a < 0 \]

Answer 26

what about something like that?

Answer 27

Let f(x)=|2x 10| and g(x)=|2x 24| . Find all values of x for which f(x)=g(x) .

Answer 28

if they are equal to each other?

Answer 29

what is |2x 10| ? Are you missing any operator ?

Answer 30

oh! oops
Let f(x)=|2x+10| and g(x)=|2x-24| . Find all values of x for which f(x)=g(x) .

Answer 31

May be you could post that as new question ...

Answer 32

i tried no one replied but ill post it again

Answer 33

If you don't get answers from this site .. post it here : math.stackexchange.com