The correct answer is: [D]: " (0, 0) " .____________________________________________________
Explanation:
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Given: " y < - 2x + 3 " ; We can rewrite this inequality as:
→ " 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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