Question

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

Answer 1

Consider the equation $\dfrac{1}{3}(n+1)=\dfrac{1}{6}(3n-5).$

1 step. Multiply this equation by 6:

$\dfrac{6}{3}(n+1)=\dfrac{6}{6}(3n-5),\\ 2(n+1)=3n-5,\\2n+2=3n-5.$

2 step. Separate expressions in such way, that variables are in the left side and the numbers are in the right side:

$2n-3n=-5-2.$

3 step. Add expressions in both sides:

$n\cdot (2-3)=-(5+2),\\-1\cdot n=-7,\\-n=-7.$

4 step. Multiply this equaiton by -1:

n=7.

Answer: n=7.

Answer 2

1/3(n+1)=1/6(3n-5)
1/3n+1/3 = 1/2n-5/6
1/3 = 1/6n - 5/6
7/6 = 1/6n
so n = (7/6) / (1/6)
     n = 7