Question

Which of the following equations have the same solution? Give reasons for your answer that do not depend on solving the equations.

A -(7-4x)=9

B 12=-4(-6x-3)

C 5x+34=-2(1-7x)

D 14=-(x-8)

E -8=-(x+4)

F x+5=-5x+5

Answer 1

none

Explanation:

A. -7+4x=9 4x=9+7 x=4

B. x= -1

C. x = -32/19

D. x = -6

E. x = -12

F. x= 0

Answer 2

A,C and E have solution x=4

B and F have solution x=0

Explanation:

We have to find the equations which have same solution.

A.
`-(7-4x)=9`

`-7+4x=9`

`4x=9+7=16`

`x=(16)/(4)=4`

B.
`12=-4(-6x-3)`

`12=24x+12`

`24x=12-12=0`

`x=(0)/(24)=0`

C.
`5x+34=-2(1-7x)`

`5x+34=-2+14x`

`34+2=14x-5x`

`36=9x`

`x=(36)/(9)=4`

D.
`14=-(x-8)`

`14=-x+8`

`x=8-14=-6`

E.
`-8=-(x+4)`

`-8=-x-4`

`x=-4+8=4`

F.
`x+5=-5x+5`

`x+5x=5-5=0`

`6x=0`

`x=(0)/(6)=0`

A,C and E have same solution because when we substitute x=4 then it satisfied the given equations.It does not depend on solving the equations.

B and F have same solution because when we substitute x=0 then it satisfied the given equations.