solve (3x/7) - (5x/3) = (2/21)?

Question

I am so lost in this class. This is part of my final and I am not doing so well.

Answer 1

To solve this, you of course must know how to add fractions:

1) You first add the left hand of the equation. Then, you'll have that (-26x/21) = (2/21)

(3x/7) - (5x/3) = (9x - 35x/21) = (-26x/21) = (2/21)

2) Once you've done that, you will have to know the value of "x":

(-26x/21) = (2/21) => -26x = (2*21/21) => -26x = 2

-26x = 2 => -x = (2/26) => x = (-2/26) = (-1/13)

3) Then, just to be sure that everything's ok, you replace "x" by the number it resulted ((-2/26) to simplify stuff as you'll see below, because (-1/13) would be a little more large, but both are the same):

(3(-2/26)/7) - (5(-2/26)/3) = (-26(-2/26)/21) = (-(-2)/21) = 2/21

NOTE: remember that the result for "x" must be (-1/13) instead of (-2/26). I just used it because it's easier than the first one to proof the equation

Answer 2

solve (3x/7) - (5x/3) = (2/21)?

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

We need to take the LCM for the two fractions on the left hand side. LCM is 7 x 3 = 21.

3x gets multiplied by 3 and 5x by 7.

(9x - 35x) / 21 = 2/21

Since the denominator is now equal, we can remove that.

9x - 35x = 2

-26x = 2

x = - 2/26 = -1/13

Answer 3

I'm assuming you mean that the slashes mean fractions...
Multiply through by the common denominator. In this case, 21.
21(3x/7)-21(5x/3) = 21(2/21)
This gives you
9x - 35x = 2
-26x = 2
x = -2/26
Reduced down to x = -1/13
Now check your work. If it doesn't work, the answer is no solution.

Answer 4

first get a common denominator (21)
do this by multiplying (3x/7) by (3/3)
(5x/3) by (7/7)
then since you have the common denominator, having the 21 is unnecessary so you can cross it out.
then the equation should look like 9x -35x=2
then subtract and get -26x=2
then divide both sides by -26 and you get x=-1/13