Question

How do you solve `\frac { y - 4} { 3} + \frac { y - 3} { 5} = \frac { y - 5} { 10} - 1`?

Answer 1

`color(purple)(y=1`

Explanation:

`(y-4)/3+(y-3)/5=(y-5)/10-1`

`:.(10(y-4)+6(y-3)=3(y-5)-30)/30`

multiply L.H.S and R.H.S. by `color(purple)30`

`:.10y-40+6y-18=3y-15-30`

`:.10y+6y-3y=-15-30+40+18`

`:.13y=-45+58`

`13y=13`

`:.color(purple)(y=1`

substitute `color(purple)(y=1`

`:.(color(purple)1-4)/3+(color(purple)1-3)/5=(color(purple)1-5)/10-1`

`:.(-3)/3+(-2)/5=(-4)/10-1`

`:.(10(-3)+6(-2)=3(-4)-30)/30`

multiply L.H.S and R.H.S. by `color(purple)30`

`:.-30-12=-12-30`

`:.color(purple)(-42=-42`