Inequality

[lesfeaves]

Is x > 0?

(1) |x + 3| = 4x – 3

(2) |x + 1| = 2x – 1
Official Answer later

[bose]

imo d
stmt 1 gives x=2 if x>-3 and 0 if x<-3 0 not possible so x=2
stmt 2 gives x=2 if x>-1 and 0 if x<-1 0 not possible so x=2

[e.cartman]

I agree with bose. Half of each stmt is a lie. Why do they lie like that!!

[rkwagle]

hi bose, why can't x<-3 ?

[e.cartman]

Bose split the equality into 2 parts. For 1st part, (x+3) is positive, which is when x>-3. For the other part (x+3) is negative, when x<-3.
(You can ignore x=-3 after checking that there won't be any solution there).

That is how the equations with modulus are solved. Sometimes solution satisfies the initial range assumption, sometimes it qualifies the range, sometimes it violates the range, sometimes you get junk results like 4=6... modulus equations & inequations are crazy!