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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