solve the inequality:
\left| x - 1 \right| + \left| 2- x \right| 3 + x

Question

solve the inequality:
\left| x - 1 \right| + \left| 2- x \right| > 3 + x

anonymous · Answer

$$\left| x - 1 \right| + \left| 2- x \right| > 3 + x$$

ash2326 · Answer

We have
$$|x-1|+|2-x|>3+x$$
There are two mods here so there are three conditions here
Let's solve for each case seperately

ash2326 · Answer

@kirmats are you here

anonymous · Answer

yupp...

ash2326 · Answer

Case 1)
x<1
Can you write the inequality for this condition

ash2326 · Answer

@kirmats Are you working on it?

anonymous · Answer

1-x+ 2-x > 3 + x
3-2x>3+x
-3x>0
x<0

ash2326 · Answer

Good work:D
So we started with the condition x< 1 and got x<0
so for this case what's the range of x?

anonymous · Answer

$$\left( -\infty, 0 \right)$$

ash2326 · Answer

Great work:D
Let's work on case 2 now
Case 2) $ x= [1, 2)$

ash2326 · Answer

Could you solve for this case?

anonymous · Answer

x-1+2-x>3+x
1>3+x
x<-2
this is where i got stuck..

ash2326 · Answer

Ok, I'll explain
We had the condition x<2 and x>=1
but we got x<-2
so in this case there is no common range, so no solution exist for this case range|dw:1337402947543:dw|