Solve for x. 7x-5 over 2 -4= 5x+2 over 3?

Question

Please help!!!

Answer 1

Oops .. I worked this out a little while ago but I didn't see the -4 on the left hnad side so I worked out the wrong question! So I am editing my reply. I just worked it out again with the -4 in there and came out with a different answer, x = 43/11, approx 3.909
Which brings up something that's been bothering me about all this. When you ask a question like this you're likely to get several different answers. How do you know which one is right? People can copy your question wrong, like I did, or they can make a mistake in the work itself, like some other people did. So how do you know which answer to use?

The only way to know for sure, is to put the result back into your question, in place of x, and see if it comes to the same number on each side. I did this, with the number I came up with, x = 43/11, and found that it came to the same number, 7 2/11, on each side. So I can be confident that I've come up with the correct answer for the question that I worked out. But is it the question that you asked? Or did you mean (7x - 5)/(2-4) = 5x + (2/3)? Or maybe ((7x-5)/2) -4 = (5x + 2)/2? Or...?

Anyhow, since I see no one else got what I got, I may as well show you how I got it...

((7x-5)/2) - 4 = (5x + 2)/3
Write the 4 as 8/2, combine the left hand side and get
((7x - 5)/2 - (8/2) = (7x - 13)/2 = (5x + 2)/3
Now multiply everything by the common denominator of 2 and 3, which is 6. This clears the fractions and gives you
3(7x-13) = 2(5x + 2) which is
21x - 39 = 10 x + 4
Subtract 10 x from each side, add 39 to each side, and you get
11 x = 43
x = 43 / 11

Or maybe you meant ( (7x -5) / 2) -4 = 5x + (2/3)?
Someone else will probably do it for you that way.

Generally, when solving for a variable, simplify each side as much as possible, then use inverse operations to get the letter by itself. Do tihs in reverse order than you use in simplifying, that is, first take care of stuff that's added or subtracted, then stuff that's multiplied or divided. Understand this and then you can do this kind of stuff for yourself, since none of us will be able to help you on your test.

Answer 2

Rewrite as: 7x - 5/-2 = 5x+2/3
First: get rid of fractions > take the denominators (-2, 3) and multiplying them by everything:

(-2)(3)(7x - 5)/2) = (-2)(3)(5x+2/3)

Second: cross cancel like terms and combine:

3(7x - 5) = -2(5x+2)
21x - 15 = -10x - 4

Third: were solving for "x" and make sure "x" is on the left:

21x + 10x - 15 = -10x + 10x - 4
31x -15 = - 4

31x - 15 + 15 = - 4 + 15
31x = 11
31x/31 = 11/31
x = 11/31

Answer 3

X=6

Answer 4

So, you have

7x-5 over 2-4 = 5x+2 over 3.
7x-5 over -2 = 5x+2 over 3 2-4=-2
21x-15 = -10x-4 Multiply both sides by -2, then 3
31x = 11
x = 11 over 31