Equation involving modulus Solve the equation , 
$|x+1| + |x-2| = |2x-1|$ 
This was the solution given in my book , 
$|x+1| + |x-2| = |2x-1|$ 
$(x+1)(x+2) ≥ 0$
Hence , $x≤-1 , x≥2$ 
However I couldn’t understand the second step. How did they just factorise the equation that was in the modulus ? I initially thought of squaring but I believe that would be too long. So , what how can we solve such modulus equations by factorization ?

we distinguish four cases:
1)$$x\geq 2$$ this is impossible
2)$$\frac{1}{2}\le x<2$$ then we have $$x+1-x+2=2x-1$$
3)$$-1\le x<\frac{1}{2}$$ we get $$x+1-x+2=-2x+1$$
4) $$x<-1$$ then we have $$-x-1-x+2=-2x+1$$
