Question

Solve 7y-6=2y+8

Show that 7/8-5/6=1/24
Show that 5/8÷7/12=1 1/14
Simplify fully v4×v7÷vt

Answer 1

Please check the explanation part for more details.

Explanation:

1. Solve
`7y - 6= 2y + 8`

Send all components contain
`y` to the left, the other components to the right:

<=>
`7y - 6 = 2y + 8`

(sign of
`2y` is changed from negative to positive, sign of
`6` is changed from negative to positive)

<=>
`5y = 14`

Divide both sides of equation by
`5`:

<=>
`y = (14)/(5)`

2. Show that
`(7)/(8) - (5)/(6) =(1)/(24)`

First, we prove that
`24` is least common multiple(LCM) of the denominators of
`2` components on the left side (
`8` and
`6`).

`8 = 2^(3)`

6 =
`2` x
`3`

=> LCM =
`2^(3)` x
`3` =
`8` x
`3` =
`24`

Multiply the first component
`(7)/(8)` by a factor which is equal to the quotient of LCM and denominator:
`(24)/(8) = 3`

=>
`(7)/(8) = (7*3)/(8*3) = (21)/(24)`

Multiply the second component
`(5)/(6)` by a factor which is equal to the quotient of LCM and denominator:
`(24)/(6) = 4`

=>
`(5)/(6) = (5*4)/(6*4) = (20)/(24)`

=>
`(7)/(8) -(5)/(6) = (21)/(24) - (20)/(24) = (1)/(24)`

3. Show that
`(5)/(8) / (7)/(12) = (11)/(14)`

`(5)/(8) / (7)/(12) =`
`(5)/(8) * (12)/(7) =`
`(60)/(56) =(60/4)/(56/4) = (15)/(14) = 1(1)/(14)`

4.
`(v4*v7)/(vt) = (v)/(v) * (v*4*7)/(t) = (v*28)/(t)`

Hope this helps!

:)