Question

find all x belongs to R that satisfy the eqaction |x+1|+|x-2|=7

Answer 1

there three cases
first if x<-1 then we can rewrite equation -x-1-x+2=7 so
-2x=6& we have x=-3 and it is <-1 so it is solution.
second -1=<x<=2
then we rewrite equation x+1+2-x=7 3=7 so there is no solution in this
case
third x>2 so x+1+x-2=7 2x-1=7& 2x=8 x=4>2

so we have two
solutions x=-3, x=4