whats the answer to 3y+2>12-y

Question

please list how you got the answer also. thank you.

Answer 1

3y + 2  > 12 - y

 

3y + 2 - 12 + y > 0  <--- everybody to left side, signs change

 

4y - 10 > 0  <---- combines like terms

 

4y > 10  <---- adds 10 to both sides

 

y > 10/4 = 5/2  <--- divides both sides by 4, then reduces to lowest terms.

 

CHECK:

 

   Let y=3:  3(3)+2 > 12 - 3 -->  9 + 2 > 12 - 3 ---> 11 > 9 YES it works

 

  Let y=0:   3(0)+2  > 12 - 0  ---> 0 + 2 > 12 - 0 --> 2 > 12 ; Fails as expected

 

  y=5/2 :   3(5/2) + 2 = 15/2 + 2 = 15/2 + 4/2 = 19/2 vs/ 12 - 5/2 = 24/2 - 5/2 = 19/2

               

y > 5/2 or (5/2, infinity)