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. [tex]-(7-4x)=9[/tex]
Taking off the brackets we get,
[tex]-7+4x=9 \Rightarrow +4x=9+7[/tex]
[tex]\Rightarrow 4x=16 \\[/tex]
[tex]\Rightarrow x=\frac{16}{4} \Rightarrow 4[/tex]
Here x=4 --- (a)
B. [tex]12=-4(-6x-3)[/tex]
Multiplying -4 inside we get,
[tex]12=+24x+12 \Rightarrow 12-12=24x[/tex]
[tex]\Rightarrow x=0[/tex]
Here x=0 --- (b)
C. [tex]5x+34=-2(1-7x)[/tex]
Multiplying -2 inside we get,
[tex]5x+34=-2+14x[/tex]
Grouping the terms,
[tex]34+2=14x-5x \Rightarrow 36=9x[/tex]
[tex]\Rightarrow x=4[/tex]
Here x=4 --- (c)
D. [tex]14=-(x-8)[/tex]
[tex]\Rightarrow 14=-x+8 \Rightarrow -x=14-8[/tex]
[tex]\Rightarrow x=-6[/tex]
Here x=-6 --- (d)
E. [tex]-8=-(x+4)[/tex]
[tex]\Rightarrow -8=-x-4 \Rightarrow x=8-4[/tex]
[tex]\Rightarrow x=4[/tex]
Here x=4 --- (e)
F. [tex]x+5=-5x+5[/tex]
[tex]\Rightarrow x+5x=5-5[/tex]
[tex]6x=0 \Rightarrow x=0[/tex]
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.
