# Trying to solve |2x-1|-|x+5|-3=0

1. Jan 11, 2016

### bonildo

1. The problem statement, all variables and given/known data
trying to solve |2x-1|-|x+5|-3=0:
2. Relevant equations
3. The attempt at a solution

for x>1/2 I got x=9

for -5<x<1/2 I got x=-7/3

but for x<-5 I got -(2x-1)-(-(x+5))-3=0 => x=3 (which is incorrect)

why x=3 is incorrect , or why I shouldn't considerate the case x<-5 ?

2. Jan 11, 2016

### Staff: Mentor

Because for that interval, (-∞, -5), you are assuming that x < -5. Therefore x cannot equal +3.

3. Jan 11, 2016

### Ray Vickson

If your assumption of x <= -5 leads to the conclusion that the root is at x = +3 (outside the starting interval), that means that there IS NO ROOT in the interval (-∞,-5). Plot a graph to see why this is so.

4. Jan 12, 2016

### symbolipoint

You should try checking conditions this way although not as efficient of choices:

2x-1 and x+5 both positive;
2x-1 and x+5 both negative;
2x-1 positive and x+5 negative;
2x-1 negative and x+5 positive.

Solve the equation in each of the four conditions and check each result.