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

2 Answers

4 votes

Answer:

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.

User Choxx
by
8.3k points
4 votes

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.

User Ehsan Foroughi
by
7.5k points

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