Question

3x - 2 (x + 3) = 4x - 7

Answer 1

The answer:   " x = ⅓ " .
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Given:  " 3x − 2 (x + 3) = 4x − 7 " ; Solve for "x" ;
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Start with the following term on the "left-hand side" of the equation:

" - 2 (x + 3) " ;
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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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As such, 

  " -2 (x + 3) = -2(x) + -2(3) = -2x + (-6) = -2x − 6 ;
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So, we can rewrite our equation:
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 " 3x − 2 (x + 3) = 4x − 7 " ; substituting:  " -2x − 6"  (for " −2 (x + 3)" ; as follows:
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   3x − 2x − 6 = 4x −  7 ; 
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On the left-hand side off the equation; 
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We can combine the "like terms" ; as follows:

  3x − 2x = 1x = x ;  and rewrite the equation:
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                    x − 6 = 4x −  7 ; 

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We can subtract "4x" from each side of the equation; and add "6" to each side of the equation:
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              x − 6 − 4x + 6 = 4x −  7 − 4x + 6 ;

to get:      -3x = -1 ; 
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Now, we divide EACH SIDE of the equation by "-3" ; to isolate "x" on ONE SIDE OF THE EQUATION; and to solve for "x" ;
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                 -3x / 3 = -1/-3 ; 
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        to get:  x = ⅓ .
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    →  Now, let us check our answer by plugging in "⅓" for all values of "x" in the ORIGINAL GIVEN EQUATION; to see if the equation holds true:
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                    →   3x − 2 (x + 3) = 4x − 7 ;

                    →  [3 * (⅓) ] − 2 [ (⅓) + 3) = ? 4(⅓) − 7 ?? ;

                    →  (1) − 2(3 ⅓) =?  (⁴/₃)  − 7 ?? ;
 
                    →  (1) − 2(3 ⅓) =?  (⁴/₃)  − 7 ?? ;

                    →    (³/₃) − 2(¹⁰/₃) =?  (⁴/₃)  − (²¹/₃) ?? ;

                    →    (³/₃) − (²⁰/₃) =?  (⁴/₃)  − (²¹/₃) ?? ;

                    →    ⁽³ ⁻²⁰⁾/₃) =?  ⁽⁴⁻²¹⁾/₃) ??

                    →   ⁻¹⁷/₃ = ? ⁻¹⁷/₃ ??  Yes!  Our answer "makes sense"!
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