How to solve this simple algebra question?

x-1/5x = 84
5/5x - 1/5x = 84
4/5x = 84
x = 84 * 5/4
x = 105

thinking about it logically, 1/5x is a fifth of an x. You subtract it from a whole x. This would obviously give you 4/5x. You then move the fraction over: Multiplication on one side turns into division on the other. In order to divide a fraction, you multiply the other side by its reciprocal, which is 5/4.

x - 1/5x = 84
5/5x - 1/5x = 84
4/5x = 84
x = 84/(4/5)
x = 84(5/4)
x = 420/4 or 105

Answer: x = 105

Proof:
105 - 1/5(105) = 84
105 - 21 = 84
84 = 84

Some of the previous answers have assumed that 1/5x is one-fifth of x, but that is not what you have written. One-fifth of x would be written as (1/5)x, not 1/5x.

If this is
x-1 over 5x equals 84 (the way you've written it),
you will end up with a quadratic equation, since to get rid of the x from the bottom you'll have to multiple all three terms by 5x, so you would get
x*5x - (1/5x)*5x = 84*5x
5x^2 - 1 = 420x.
Rearrange and get
5x^2 - 420x - 1 = 0.
This looks like a weird sort of problem for them to be giving you, though it can be solved by the quadratic formula and will have two roots.

Or is this problem really
x - (1/5)x = 84 ??
Then you could say, since 1/5 = 0.2,
x - 0. 2x = 84 or
0.8x = 84 and that is easy to solve.

Multiply both sides by 10 to get rid of the decimal point and you get
8x = 840 so
x = 105.

These are my best guesses at what you are being asked to solve.
If I'm understanding the way you've written it out, it really looks unlikely that they would give you such a weird problem since it results in a quadratic that doesn't seem like it has any obvious factors and then needs the quadratic formula to solve.
The second way looks like a much more likely problem. Check the parentheses on the original problem that you have to make sure and see if there are actually parentheses around the (1/5). If not, maybe the teacher made a typo.
I can see why you're confused. Good luck.

x

The first thing you must learn is how to present a question correctly by using brackets :-
x - (1/5) x = 84
(4/5) x = 84
x = 420 /4
x = 105

(x - 1)/5x = 84
x - 1 = 5x(84)
x - 1 = 420x
x - 420x = 1
-419x = 1
x = -1/419

Well, I can't clearly get that 1/5 x , whether it's one & a half (though that way it should be 1.5...) or , one-fifth , anyway , i'll solve it in both ways :
#1-(1/5 thought as one-fifth)
x-1/5x=84
5/5x-1/5x=84
4/5x=84
x=84÷4/5=84*5/4
x=105
------------------------------------------------------------------------------------------------------------
#2-
x-1.5x=84
1x-1.5x=84
-0.5x=84
x=84÷-0.5
x=-168

That's it! :-)

Whenever there is a variable by itself there is a 1 in front of it. So, you have:
1x-1/5x=84
0.8x=84
then, you divide by 1/5 on both sides to get the x by itself
0.8x/0.8=84/0.8
x=105

x - 1/5x = 84
(x - 1/5x)x = 84x
x^2 - 1/5 = 84x
x^2 - 84x - 0.2 = 0
(x - 42)^2 = 42^2 + 0.2
x - 42 = -+ root of [42^2 + 0.2]
x ~ 84

times it by x.
x^2 - 1/5 = 84x
x^2 - 84x - 1/5 = 0
Using the formula...
x = (84 + sqrt(84^2 - 4.1/5))/2 or
x = (84 - sqrt(84^2 - 4.1/5))/2

it should be 4/5x = 84 (because if you have 1 times x or 5/5x and subtract 1/5 of the x it would leave 4/5 x), then divide 84 by 4/5.. so i guess times 4 divided by 5. try that.