Question

Consider the following equation.

12w - 27 = -34 + 14w

Select the equation that has the same solution as the given equation above.

A. -2w + 21 = -8w + 36

B. -5/6w + 2 = 13/3 - 1/6 w

C. -47 - 10w = -9w - 40 - 3w

D. 9/7w = 13/14w + 2

Answer 1

The answer is C

12w - 27 = -34 +14w

-2w = -7

w = 7/2

-47 - 10w = -9w -40 - 3w

-47 - 10w = -12w - 40

-7 = -2w

w = 7/2

Answer 2

Option C is the correct answer.

Explanation:

The equation is given as :

`12w-27=-34+14w`

Solving this by pairing the like terms together,

`12w-14w=-34+27`

`-2w=-7`

This gives
`w=(7)/(2)`

Now, we will solve all the equations to check which is same as the above.

A.

`-2w+21=-8w+36`

=>
`-2w+8w=36-21`

=>
`6w=15`

=>
`w=(15)/(6)=(3)/(2)`

This is the wrong option.

B.

`(-5w)/(6)+2=(13)/(3)-(w)/(6)`

=>
`(-5w+12)/(6)=(26-w)/(6)`

=>
`-5w+12=26-w`

=>
`-5w+w=26-12`

=>
`-4w=14`

=>
`w=(-14)/(4) =(-7)/(2)`

This is the wrong option.

C.

`-47-10w=-9w-40-3w`

=>
`-10w+9w+3w=-40+47`

=>
`2w=7`

=>
`w=(7)/(2)`

This is the right option.

D.

`(9w)/(7)=(13w)/(14)+2`

=>
`(9w)/(7)=(13w+28)/(14)`

=>
`126w=91w+196`

=>
`35w=196`

=>
`w=(196)/(35)`

Dividing by 7, we get

=>
`w=(28)/(5)`

This is the wrong option.

Therefore, option C is the correct answer.