Question

Solve 4(x - 3) - 2(x - 1) > 0.

Answer 1

The answer is:  [C]:  "  {x | x > 5} "  .
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Explanation:
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Given:   " 4(x − 3) − 2(x − 1) > 0 " ; 
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Note the "distributive property of multiplication" :
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             a(b+c) = ab + ac ;
             a(b−c) = ab − ac ;
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So, given:
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                   →     4(x − 3) − 2(x − 1) > 0 ; 
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Let us simplify; and rewrite:
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Start with: 
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                   →    -2 (x − 1) = (-2*x) − (-2 *1) = -2x − (-2) = -2x + 2 ;
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Now, continue with:

                   →   4(x − 3) = (4*x) − (4*3) = 4x − 12 ;
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So, given the original problem: 
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                   →   4(x − 3) − 2(x − 1) > 0 ; 
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Rewrite;

Replacing:  "4(x − 3)" ;  with: "4x − 12" ;

and replacing "− 2(x − 1)" ; with: " -2x + 2" ;
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 as follows:    →  " 4x − 12 − 2x + 2 " > 0 ;
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On the "left-hand side", combine the "like terms", and simplify ;
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                  +4x −2x = +2x ;  −12 +2 = -10 ;   and rewrite:
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               →   2x − 10 > 0 ;   Add "10" to EACH SIDE of the inequality;
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               →   2x − 10 + 10  >  0 + 10 ; 
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to get:     →   2x  > 10 ;
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               →    Now, divide EACH SIDE of the inequality by "2";
to isolate "x" on one side of the inequality; & to "solve"/"simply" for "x" ;
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               →    2x / 2  > 10 / 2 ;
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               →        x > 5  ;    which is: 
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               → Answer choice: [C]:  "  {x | x > 5} "  .
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