Question

Solve: `(6x + 1)/3 + 1 = (x - 3)/6`

Answer 1

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)