Question

i'm don't understand how to solve this (image attached). can someone please clarify and show me how to find the answer?

Answer 1

a >=0
b >= 0
c >= 0
c = ax - bx
so we can factor out an x
c = x ( a - b )

Answer 2

how can we "solve" for x ? @one2345 do you know?

Answer 3

How can we put it in the form x = ...

Answer 4

we divide (a-b) on both sides to put x by itself?

Answer 5

Right! Lets divide both sides by (a-b)
x = c / (a - b)

Answer 6

So it would help if we could show that there is more than one solution
if a-b = 1
and c = 0

What does x = ?

Answer 7

x = 0

Answer 8

Yep! if a = b then we are going to be dividing by 0
there will be no solution

if a= b
(a-b) x = c
if a-b equals 0
and c = 0

x could be anything so if a= b
c has to equal zero

if a-b = 1 then x = c so if c does not equal 1 it could equal anything
so that would not be a solution or that would be more than 1 solution

The very last option has only one solution, x= 0

Answer 9

So let me explain it briefly one more time:
The first and last one both force x to equal zero
if something nonzero multiplied by x = 0 then x has to equal zero

For the 3rd one, 0x=0 means x can equal anything

and for the fourth one, x = c means x can equal anything (except 1)

the 2nd one has 0 x = something and that one is not possible
since 0 times anything equals zero.

They definitely want #3 & #4 since they allow x to equal anything
The first and last allow x to also equal zero... So I don't think we have to exclude them
So it's either 3&4, or 1345

Answer 10

yes, i understand it now. thank you very much for your help!

Answer 11

yw :)