Answer: "x = 15 " .
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Explanation:
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Given:
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" (x + 3) / 6 = (x − 6) / 3 " ; Solve for "x" ;
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Multiply EACH SIDE of the equation by "6" ;
to get rid of the "denominators" ("fractions") :
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→ 6* { (x + 3) / 6 } = 6 * { (x − 6) / 3 } ;
to get:
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→ x + 3 = 2(x − 6) ;
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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:
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→ 2(x − 6) = (2*x) − (2* 6) = 2x − 12 ;
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So; we can rewrite the original equation:
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" x + 3 = 2(x − 6) " ;
→ by substituting: "2x − 12" ; [ in lieu of: "2(x − 6)" ] ; as follows:
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→ x + 3 = 2x − 12 ;
Now, we can subtract "x"; and can add "12" ; to EACH SIDE of the equation:
→ x + 3 − x + 12 = 2x − 12 − x + 12 ;
to get: 15 = x ;
↔ x = 15 ; which is our answer.
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