The answer is: [C]: x < 7 .
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Explanation:
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Given:
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12x – 3x + 11 > 4x – (17 – 9x) ;
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We need to simplify EACH side of the inequality; and then rewrite:
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Let us start with the "left-hand side" :
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12x – 3x + 11
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We see that among the three terms, there are 2 (two) "like terms";
"12x" and "-3x" ;
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So, 12x – 3x = 9x ; and bring down the remaining term, " +11" ;
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9x + 11 ;
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Now, let us simplify the 'right-hand side' of the inequality:
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4x – (17 – 9x) ;
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Treat this expression as:
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4x – 1(17 – 9x) ;
(Note: The coefficient "1" is implied; since anything multiplied by "1" is that same value").
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Note the "distributive property of multiplication" :
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a* (b + c) = ab + ac ; AND:
a* (b – c) = ab – ac ;
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So, we have the expression:
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4x – 1(17 – 9x) ;
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Take the: -1*(17 – 9x); and simplify;
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-1*(17 – 9x) = (-1 * 17) – (-1 * 9x) = -17 – (-9x) = -17 + 9x ;
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We have:
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-17 + 9x ; Rewrite as: 9x – 17
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Now, bring down the "4x"; and rewrite the expression:
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9x – 17 + 4x ;
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Notice that there are 2 (two) "like terms" out of the 3 (three) terms in this expression:
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+9x and +4x ;
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Combine these like terms; and simplify:
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4x + 9x = 13x ;
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Now, bring down the "– 17 " ; and rewrite the entire "right-hand side" expression:
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13x – 17 ;
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Now, we can rewrite the entire equality, by substituting our simplified expressions:
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9x + 11 > 13x – 17 ; Now, solve for "x" ;
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Subtract "9x" from EACH side; and add "17" to EACH side;
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9x + 11 – 9x + 17 > 13x – 17 – 9x + 17 ;
28 > 4x ;
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Now, divide EACH side of the inequality by "4", to isolate "x" on one side of the inequality; and to solve for "x" ;
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28 / 4 > 4x / 4 ;
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7 > x ; or, write as: x < 7 ; which is: "Answer choice: [C] ".
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