What is the solution set for the following inequality?

Question

|7x-3|>=5

Answer 1

 

7x - 3 >= 5   OR  7x-3 <= -5

 

7x >= 8 OR 7x <= -2

 

x >= 8/7  OR x <= -2/7

 

closed circle at -2/7 then shade left

closed circle at 8/7 then shade right

 

CHECK:

 

   -1 is in the first set:   | 7(-1) - 3| =| -7 - 3 | = |-10| = 10 >= 5 ;  yes it works

  2 is in the second set:  | 7(2) - 3 |  = | 14 - 3 | = | 11 | = 11 >= 5  ; yes it works

  zer0 is NOT in either set:  | 7(0) - 3 | = | 0 - 3 | = | -3 | = 3 < 5  ; No, it fails as expected

 

 Moreover, For x = -2/7,  | 7(-2/7) - 3 |  = | -2 - 3 | = | -5 | = 5 >= 5 ; yes it works

                For x = 8/7,  | 7(8/7) - 3 | = | 8 - 3 |  = | 5 | = 5 >= 5 ; yes it works