Home / Assignment Help / Which of the following is a solution to the inequality y

Which of the following is a solution to the inequality y

The correct answer is:  [D]:  ” (0, 0) ” .____________________________________________________
Explanation:
____________________________________________________
Given:   ” y

                                →   ” y <  3 − 2x ” ;
____________________________________________________
Consider:  Choice [A]:  “(1, 1)” ; that is, ” x = 1,  y = 1″ .
                                
      When x = 1 ; does y = 1 ; make sense, for this inequality;
____________________________________________________
      →        ” y <  3 − 2x ” ?

      1 < 3 − 2(1) ? ;  1 < 3 − 2 ? ;  1 < 1 ?  No!  {” 1 = 1″.} .

      →  So;  Answer choice:  [A]:  ” (1, 1) ” ;  is INCORRECT.
____________________________________________________
Consider:  Choice [B]:  (3, 0) ” ; that is, ” x = 3,  y = 0″ .
                                
       When x = 3 ; does y = 0 ; make sense, for this inequality;
____________________________________________________
       ” y <  3 − 2x ” ?

      0 < 3 − 2(3) ? ;  0 < 3 − 6? ;  0 < -3 ?  No!  {” 0>3″.} .

      →  So;  Answer choice:  [B]:  (3, 0) ” ;  is INCORRECT.
____________________________________________________
Consider:  Choice [C]:  ” (- 3, 10) ” ; that is, ” x = – 3,  y = 10″ .
                                
      When x = – 3 ; does y = 10 ; make sense, for this inequality;
___________________________________________________
      →        ” y <  3 − 2x ” ?

      10 < 3 − 2(-3) ? ; 
                    →  10 < 3 − 2(-3) ? ;  
                    →  10 < 3 − (-6) ? ; 
                    →  10 < 3 + 6 ? ;  →  10 < 9 ?  No!  {“10 > 9”.} .

      →  So;  Answer choice:  [C]:  ” (-3, 10) ” ;  is INCORRECT.
___________________________________________________
Consider:  Choice [D]:  ” (0, 0) ” ; that is, ” x = 0,  y = 0″ .
                                
When x = 0 ; does y = 0 ; make sense, for this inequality;
___________________________________________________
       ” y <  3 − 2x ” ?

      0 < 3 − 2(0) ? ;  0 < 3 − 0 ? ;  0 < 3 ?  Yes!
____________________________________________________
So; the correct answer is:  [D]:  ” (0, 0) ” .
____________________________________________________

About eduhawks

Check Also

Are the phases of the moon the same everywhere on earth

Are the phases of the moon the same everywhere on earth