Please Help. Thanks!

Question

If x/8>x, which could be a value for x?

a. -1

b. 0

c. 2

d. 1/4

Answer 1

x/8 > x

multiply both sides by 8

x > 8x

divide both sides by x

1> 8 which is impossible, if x >0 or if x=0

but if x<0 then x/8 >x

a is correct

just plug in each answer and only a works

-1/8 > -1

but 0/8 is not greater than 0, 0=0 0 is not greater than 0

2/8 = 1/4 is not greater than 2

and

1/4/8= 1/32 is not greater than 1/4

Answer 2

x/8 > x      Let’s multiply by 8 on both sides

 x > 8x      

-x   -x       Subtract x on both sides (* See note below)

----------

0 > 7x      

7x < 0       Flip

7x < 0     Divide by 7 on both sides

x < 0  Our answer has to be less than 0, so the -1 in Choice A is the answer.

An alternative way of solving this is to plug in the answer choices.

*at this step, we cannot divide by x on both sides, because this is an inequality and we don’t know if x is positive or negative. If it’s negative, we would have to flip the inequality symbol.