Question

How do you solve `-\frac { 1} { 3} u - \frac { 7} { 5} = \frac { 1} { 3}`?

Answer 1

`-1/3 u=-u/3`
`-u/3-7/5=1/3`
Add `7/5` to both sides
`-u/3-cancel(7/5)+cancel(7/5)=1/3+7/5`
You get
`-u/3=1/3+7/5`
Now this can be done in two ways,

`color(red)(1^(st))` way
Find the LCM of 3 and 5, it is 15
`-u/3=(1xx5)/(3xx5)+(7xx3)/(5xx3)`
Multiply
`-u/3=5/15+21/15`
Add them
`-u/3=26/15`
Multiply by 3 on both sides
`-u/cancel3 xx cancel3=26/(cancel15^5) xx cancel3`
You get
`-u=26/5`
Multiply by `-1` on both sides
`-uxx-1=26/5xx-1`
`u=-26/5`

`color(red)(2^(nd))` Way
This is being continued from `-u/3=1/3+7/5`
Now, subtract `1/3` from both sides
`-u/3-1/3=cancel(1/3)-cancel(1/3)+7/5`
You get
`(-u-1)/3=7/5`
Multiply by 3 on both sides
`(-u-1)/cancel3 xx cancel3=7/5xx3`
You get
`-u-1=21/5`
Add by 1 on both sides
`-u-cancel1+cancel1=21/5+1`
`1=1/1,2/2,3/3,4/4,5/5.......`
`-u=21/5+5/5`
You get
`-u=26/5`
Multiply by `-1` as we did above
`-uxx-1=26/5xx-1`
`u=-26/5`