Maths Paper 3 doubt

[elbeyon]

Can someone out there please help me with the inequality
l x − 2 l < 3 − 2x. I used to solve these kinda problems with the general method of squaring on both side but the answer to this question does not matches to that of the marking scheme. The ms suggests the answer to be just x < 1 but I got x < 1 and x > 5/3 , now how am I supposed to eliminate the 5/3 part ? Please help asap. Thanks in advance .

 

[SalmanslK]

l x − 2 l < 3 − 2x
x-2<3-2x or -(x-2)<3-2x
-5<-3x or -x+2<3-2x
5/3>x or -1<-x ==> x<1 & x<1.67 (5/3=1.67)

Hence we can simply say x<1 ; no need to write x<1.67.

 

[Ujjwal Basnet]

l x − 2 l < 3 − 2x
x-2<3-2x or -(x-2)<3-2x
-5<-3x or -x+2<3-2x
5/3>x or -1<-x ==> x<1 & x<1.67 (5/3=1.67)

Hence we can simply say x<1 ; no need to write x<1.67.

Should not it be X<1.67 ? Because for x<1 & x<1.67,if we write x<1 then are not we omitting the values bigger than 1 and smaler than 1.67?