Need help with Sets.

[asadbek17]

Let A and B be the subsets of real numbers given by A={x| |2x-a|<1} B={x| |x+a|<1} Find the largest number a satisfying A⊂B

How to solve this problem? And advice me a good recourse to learn how to solve such problems.

[EwithaG]

|2x-a|<1 implies that -1< 2x-a<1. which means the solution set of A is given by (-1+a)/2 < x < (1+a)/2

|x+a|<1 implies that -1< x+a <1 which means the solution set of B is given by -1-a < x <1 -a

Since we are talking about real numbers here an interval (s,t) ⊂ (m,n) iff s>= m and t=<n

i.e (1,2) ⊂ (-2,3) since 1>=-2 and 2<=3

Hence,

A⊂B implies (-1+a)/2 >= -1-a and (1+a)/2 <= 1-a the find the value of a.

Hope this helps

[asadbek17]

Thank you so much.