Question

|x+5| - 2|x| = 1
This shoul be easy but I'm stuck and need some help

Answer 1

Hmm, yeah, the ones with two absolute value expressions can be tricky.
You have to consider all the possibilities of what might be in the ||'s

Answer 2

yeah it is not that easy. you have to check cases

Answer 3

e.g. (x+5) and (x) could both be positive, both negative, one pos. the other neg. etc.

Answer 4

yea, I'm aware of this

Answer 5

maybe it would be best to start with
\[y=|x+5|\] and \[y=2|x|+1\] and see where they intersect

Answer 6

Then write the four different equations and solve each independently, then go back to the original statement to check the solutions.

Answer 7

^^ good tip.

Answer 8

first one is \(y=x+5,x\geq -5, y=-x-5, y<5\) second one is \(2x+1\) or \(-2x+1\) depending on whether \(x\geq 0\) or \(x< 0\)
on one of these intervals there will be no solution i believe