Question

PLease help.. |x|+|x-2|=2 and |x+2|+|x-4|=2

Answer 1

are these two separate problems?

Answer 2

yes

Answer 3

if \(x\) is any number between 0 and 2, then \(|x|=x\) and \(|x-2|=2-x\) and so \(|x|+|x-2|=x+2-x=2\) for all number in that interval

Answer 4

however if \(x\) is less than 0, then \(|x|=-x\) and so \(|x|+|x+2|=-x+2-x=-2x+2\)
not possible for negative values of \(x\)
try again with \(x>2\) and you will see it is also not possible
so the solution is all numbers between 0 and 2 or
\[0\leq x\leq 2\] or
\[[0,2]\]depending on how you would like to write it

Answer 5

ok but what about for the second equation