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# Which of the following is a solution to the inequality y

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

→   ” y <  3 − 2x ” ;
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Consider:  Choice [A]:  “(1, 1)” ; that is, ” x = 1,  y = 1″ .

When x = 1 ; does y = 1 ; make sense, for this inequality;
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→        ” y <  3 − 2x ” ?

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

→  So;  Answer choice:  [A]:  ” (1, 1) ” ;  is INCORRECT.
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Consider:  Choice [B]:  (3, 0) ” ; that is, ” x = 3,  y = 0″ .

When x = 3 ; does y = 0 ; make sense, for this inequality;
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” y <  3 − 2x ” ?

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

→  So;  Answer choice:  [B]:  (3, 0) ” ;  is INCORRECT.
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Consider:  Choice [C]:  ” (- 3, 10) ” ; that is, ” x = – 3,  y = 10″ .

When x = – 3 ; does y = 10 ; make sense, for this inequality;
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→        ” 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.
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Consider:  Choice [D]:  ” (0, 0) ” ; that is, ” x = 0,  y = 0″ .

When x = 0 ; does y = 0 ; make sense, for this inequality;
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” y <  3 − 2x ” ?

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