inequality problem

Question

LEt M and m be the largest and smallest integers satisfying the following inequalities
4x-1<2x+3
(x-3)/2 + 4/3 ≤ (2x+4)/3

Find M-m

Answer 1

4x - 1 < 2x + 3

 

     2x < 4

 

       x < 2

 

 

(x-3)/2 + 4/3 ≤ (2x+4)/3

 

3(x-3) + 8 ≤ 2(2x+4)

 

        3x - 1 ≤ 4x + 8

 

             -x ≤ 9

 

              x ≥ -9

 

So, -9 ≤ x < 2    Therefore, M = 1 and m = -9

 

M - m = 1 - (-9) = 10