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

Answer:

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,

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

$\Rightarrow 4x=16$

$\Rightarrow x=\frac{16}{4} \Rightarrow 4$

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.