6/7y+1/6(y-7)=y+1/4
(6/7)y + 1/6(y - 7) = y + 1/4
Eliminate the fractions before doing
anything else. The denominators are
6, 7 and 4. Factors are 2 * 3, 7, 2 * 2.
We don't need the third 2. 2 * 3 * 7 * 2 = 84.
Multiply the entire equation by 84.
84 * ((6/7)y + 1/6(y - 7)) = (y + 1/4) * 84
12 * 6y + 14(y - 7) = 84y + 21
72y + 14y - 98 = 84y + 21
86y - 84y = 21 + 98
2y = 119
y = 59.5
Check it with the original equation.
(6/7)y + 1/6(y - 7) = y + 1/4
(6/7)59.5 + 1/6(59.5 - 7) = 59.5 + 1/4
51 + 1/6(52.5) = 59.5 + 0.25
51 + 8.75 = 59.75
59.75 = 59.75