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

A,C and E are equal with 4 as their solution; F and B are equal with 0 as their solution. D is independent.

Solution:

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

Taking off the brackets we get,

`-7+4x=9 \Rightarrow +4x=9+7`

`\Rightarrow 4x=16 \\`

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

Here x=4 --- (a)

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

Multiplying -4 inside we get,

`12=+24x+12 \Rightarrow 12-12=24x`

`\Rightarrow x=0`

Here x=0 --- (b)

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

Multiplying -2 inside we get,

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

Grouping the terms,

`34+2=14x-5x \Rightarrow 36=9x`

`\Rightarrow x=4`

Here x=4 --- (c)

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

`\Rightarrow 14=-x+8 \Rightarrow -x=14-8`

`\Rightarrow x=-6`

Here x=-6 --- (d)

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

`\Rightarrow -8=-x-4 \Rightarrow x=8-4`

`\Rightarrow x=4`

Here x=4 --- (e)

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

`\Rightarrow x+5x=5-5`

`6x=0 \Rightarrow x=0`

Here x=0 --- (f)

So, from the above calculations we can conclude that (a), (c) and (e) are equal and (f) and (b) are equal but (d) is independent because it has a different solution.