5/21x = 2/3x - 1/7 i think i got first step?

. .5 . . . .2 . . .1 . . . .5 . . . . 2 . . .1
—— = —— - — or ——x = —x - —
.21x . . .3x . . 7 . . . 21 . . . .3 . . .7

Case 1:
. .5 . . . .2 . . .1
—— = —— - —
.21x . . .3x . . 7

. .5 . . . .2(7) . . .1(3x)
—— = ——— - ———
.21x . . .3x(7) . . 7(3x)

. .5 . . . 14 . . .3x
—— = —— - ——
.21x . . 21x . .21x

. .5 . . . 14 - 3x
—— = ———— . . . . . <- multiply both sides by 21x
.21x . . . .21x

5 = 14 - 3x

5 - 14 = -3x

-9 = -3x . . . . . . . . . . . <- divide both sides by -3

3 = x

x = 3


Case 2:
. 5 . . . . 2 . . . 1
——x = —x - —
.21 . . . .3 . . . 7

.5x . . . 2(7)x . . 1(3)
—— = ——— - ——
.21 . . . .3(7) . . .7(3)

.5x . . . 14x . . 3
—— = —— - ——
.21 . . . .21 . . .21

.5x . . . 14x - 3
—— = ———— . . . . . <- multiply both sides by 21
.21 . . . . . 21

5x = 14x - 3

5x - 14x = -3

-9x = -3 . . . . . . . . . . . <- divide both sides by -9

. . . -3
x = —
. . . -9

. . . 1
x = —
. . . 3



Done

this is what i think of. you have money of afterlife money. Cussing expenses 3 money, adultery expenses twenty. in case you finally end up with a minimum of a greenback on the top you get to circulate to heaven. in case you finally end up owing money you visit hell. Or some thing like that.

5/21x = 2/3x - 1/7
5/21x - 2/3x = - 1/7
- 9/21x = - 1/7
9/21x = 1/7
(21/9)9/21x = (21/9)1/7
x = 1/3.

Should be shown as :-

(5/21) x = (2/3) x - 1/7

5x = 14 x - 3

9 x = 3

x = 1 / 3

5/(21x) = 2/x - 1/7
21x[5/(21x)] = 21x(2/x - 1/7)
5 = 42 - 3x
3x = 42 - 5
x = 37/3

5/21x = 2/3x - 1/7

Solution:

x = 1/3

or

x = 0.333333

Anthony, Stephani and foododor . . . above are right.

2/3x - 5/21x = 1/7
14/21x - 5/21x =1/7
9/21x = 1/7
9x= 3
x = 1/3

check:

5/63 = 2/9 -1/7
5/63 = 14/63 - 9/63
5/63 = 5/63

To look at it a bit easier, convert all the fractions to have a common denominator.

5/21x = 14/21x - 3/21

since there is a common denominator throughout the equation, you can get rid of the denominator

5x = 14x -3

Solve for x.

-9x = -3
x = 1/3

Check your work:

(5/21)(1/3) = (2/3)(1/3) - (1/7)

(5/63) = (2/9)- (1/7)
convert to same denominator

(5/63) = (14/63) - (9/63)
(5/63) = (5/63)

Also, you do not divide by 3x because there is no 3x in (1/7) and when you multiply or divide the equation, you must apply it to the ENTIRE equation. Good idea though.

Your first step is wrong.

And I can't tell for sure what the first two expressions of your equation are. For instance, the first one, is that 5 divided by 21x or is that 5x divided by 21? In other words is the x in the numerator or the denominator? I suspect it is the former(numerator) but you have it written as the latter.
Assuming you have it written correctly, your first step should be to multiply all the terms in the equation by 21x so that you get

5 = 14 - 3x

I will let you finish the problem.

to get rid of all of the fractions multiply the whole thing by gcf. so you get 21(5/21x)=21(2/3x)-21(1/7) which works out to be
5x=14x-3, then isolate the x to get 3=9x, then divide by 9 to get x=1/3

Sorry, Greatest common factor would be 21.