Question

2/3w - 1/4 = 2/3 (w - 1/4)

Answer 1

No solution

Step-by-step solution:

We are given an expression:

`(2)/(3) w-(1)/(4) =(2)/(3) (w-(1)/(4) )`

We have only one variable
`w` so we will make
`w` the subject and solve for it.

`(2)/(3) w-(1)/(4) =(2)/(3) (w-(1)/(4) )`

Solving the brackets first to get:

`(2)/(3) w -(1)/(4) =(2)/(3) -(1)/(6)`

Taking LCM on both sides to get:

`(8w-3)/(12) =(4w-3)/(6)`

By cross multiplication:

`6(8w-3)=12(4w-3)`

`48w-18 = 48w -36`

`48w - 49w -18 + 36 = 0`

`w` gets cancelled so we are left with
`18\\eq 0`

Therefore,
`w` has no solution.

Answer 2

Given problem is

`(2)/(3)w-(1)/(4)=(2)/(3)\left(w-(1)/(4)\right)`

Here unknown variable is w so we will solve this equation for w.

Common denominator for given denominators 3 and 4 is 12 so we can multiply both sides by 12 so that we can cancel out all the fractions

`(2)/(3)w\cdot12-(1)/(4)\cdot12=(2)/(3)\cdot12\left(w-(1)/(4)\right)`

`(24)/(3)w-(12)/(4)=(24)/(3)\left(w-(1)/(4)\right)`

`8w-3=8\left(w-(1)/(4)\right)`

`8w-3=8w-(8)/(4)`

`8w-3=8w-2`

`8w-8w=3-2`

`0=1`

We know that 0=1 is not possible

Hence there is no solution for w.