How do you solve this equation 3/7w - 2/9 = 4/9w + 1/7?

3/7w - 2/9 = 4/9w + 1/7

Move the 4/9w to the other side through subtraction:

3/7w - 4/9w - 2/9 = 1/7

Now, while you're at it, move the -2/9 to the other side through addition:

3/7w - 4/9w = 1/7 + 2/9

Remember how to add/subtract fractions? Find the LCM and do it from there. You should get:

(27 - 28)w / 63 = (9 + 14) / 63

-w / 63 = 25 / 63

Cross multiply:

-63w = 63*25
-63w = 1575

w = -25

Question is incorrect as it stands. Should be:-
(3/7)w - 2/9 = (4/9)w + 1/7
27w - 14 = 28w + 9
- 23 = w

assuming that the unknown "w" is in the denominator, you can combine terms by subtracting (or adding) like terms.
3/7w - 4/9w=1/7 + 2/9
Using LCD (lowest common denominator of 63 (9 x 7)
27/63w - 28/63w = 9/63 +14/63
Multiplying both sides by 63w
27 - 28 = 9w + 14w
-1 = 23w
w = -1/23

Proof
3/7 (-1/23) - 2/9 = 4/9 (-1/23) + 1/7
-69/7 - 2/9 = -92/9 + 1/7
LCD of 63
-621/63 - 14/63 = -644/63 + 9/63
-635/63 = -635/63

(3/7)w - 2/9 = (4/9)w + 1/7
3w/7 - 2/9 = 4w/9 + 1/7
63(3w/7 - 2/9) = 63(4w/9 + 1/7)
27w - 14 = 28w + 9
27w - 28w = 14 + 9
-w = 23
w = 23/-1
w = -23

i think this is the way that it is meant to be solved...

3/7w - 2/9 = 4/9w + 1/7
=27w - 14 / 63 = 28w + 9 / 63 ( both the 63's get cancelled since they have the same denominators. )
=27w - 28w = 9 + 14 ( you bring the 28w to the other side and change signs... that means, = 28w will become - 28w. )
= - w = 23
therefore, w = - 23 ( ANSWER )
please tell me if i am right. hope i helped!!!

Here's how to work out the equation:

Get the numbers with "w" following on the left side and the numbers not followed by a "w" on the right:

3/7w - 4/9w = 1/7 - 2/9

Next, take out the w on the left side:

w(3/7 - 4/9) = 1/7 - 2/9

Now, get the denominators to equal the same number, 63, by multiplying each number with a 7 as the denominator by (9/9) and each number with a 9 as the denominator by (7/7).

w( (3/7)*(9/9) - (4/9)*(7/7) = 1/7*(9/9) - 2/9* (7/7)

Now, carry through with the multiplications to get:
w( (27/63) - (28/63) ) = (9/63) - (14/63)

This allows:
w(-1/63) = (-5/63)

Now, divide the right side by the (-1/63) to get w by itself.

w = (-5/63) / (-1/63)

Solve for w.

w = 5

Hope this helps :)

Make sure they have the least common denominator. In this case, it would be 63 (9 and 7 both go into 63)
so it would be 27/63w - 14/63 = 28/63w + 9/63
Simplify it by putting the w's on one side and the rest on the other (don't forget to change the symbols. make + a - if it is going to the other side, etc.)

27/63w - 28/63w = 14/63 + 9/63
simplify
-1/63w = 23/63
From there, multiply both sides by -64/1 (to make the w stand alone and be positive)
w= 23/63 * -63/1
w= -23

Seperate terms with w from those without:
3/7w - 2/9 = 4/9w + 1/7 becomes 1/7 + 2/9 = 3/7w - 4/9w
Combine mixed fractions:
1/7 + 2/9 = 3/7w - 4/9w becomes 23/63 = -w/63
Simplify to get w=-23

You multiply each side of the equation by the least common denominator.

The way you have the fractions written/typed, the denominators are: 7w; 9; 9w; 7. [The LCD would be 63w.]

If you meant for your equation to be
(3/7)w - 2/9 = (4/9)w + 1/7

then your LCD would be 63.

What he said. And bring everything under the common denominator 63.