Which of the following is a solution to the inequality y < –2x + 3?

a. (1,1)

b. (3,o)

c. (-3,10)

d. (0,0)

The correct answer is:  [D]:  " (0, 0) " .
Explanation:

Given:   " y <  - 2x + 3 "  ;  We can rewrite this inequality as:

                                →   " 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) " .

X2 - 8x + 15 = 0
(x  - 3)(x - 5) = 0
critical points are at 3 and 5