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

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.

Taking off the brackets we get,

Here x=4 --- (a)

B.

Multiplying -4 inside we get,

Here x=0 --- (b)

C.

Multiplying -2 inside we get,

Grouping the terms,

Here x=4 --- (c)

D.

Here x=-6 --- (d)

E.

Here x=4 --- (e)

F.

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.