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

[bonildo]

Homework Statement

trying to solve |2x-1|-|x+5|-3=0:

Homework Equations

3. The Attempt at a Solution [/B]
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 ?

 

[Mark44]

Homework Statement

trying to solve |2x-1|-|x+5|-3=0:

Homework Equations

3. The Attempt at a Solution [/B]
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 ?

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

 

[Ray Vickson]

Homework Statement

trying to solve |2x-1|-|x+5|-3=0:

Homework Equations

3. The Attempt at a Solution [/B]
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 ?

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.

 

[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.