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# Reducing Equations to Simpler Form

#### notes

For example : (6x + 1)/ 3 + 1 = (x - 3)/6
Solution : Multiplying both sides of the equation by 6,
(6(6x + 1))/3 + 6 xx 1 = (6(x - 3))/6
or 2 (6x + 1) + 6 = x – 3
or 12x + 2 + 6 = x – 3            (opening the brackets )
or 12x + 8 = x – 3
or 12x – x + 8 = – 3
or 11x + 8 = – 3
or 11x = –3 – 8
or 11x = –11
or x = – 1
Check:  LHS

= (6(-1) + 1) / 3 +1 = (-6+1)/3 + 1 = -5/3 + 3/3 = (-5+3)/3 = -2/3

RHS = ((-1)-3) /6 = -4 / 6 = -2/3

LHS = RHS. (as required)

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