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Maria S. gave a good explanation. I would add the following details though:

If you move numbers from one side to another, you have to change its sign. In your question, we have 4x - 102 + 63. -102 is going to become positive, and +63 is going to be negative. Therefore:

4x = 102 - 63

You can do 102 - 63 by hand if you find the mental math a bit too difficult here. 

I'd also like to add that you want 4x to become x on its own (since we want an answer of x = something). In algebra, when a number and a letter are beside each other, like 4x, that actually means 4 times x. Now, to get rid of the 4, we need to do its opposite. The opposite of multiplying is dividing, so we're going to divide 4x divided by 4. The two 4s will cancel out, leaving only x on the left side.

Finally, if we did something to the left side, we are forced to do it to the right side as well. So, you must divide 39 by 4. Dividing and fractions are actually the same thing, so 39 divided by 4 can be written as 39/4. Since 39/4 cannot be simplified, you can leave it written that way on the right side. Therefore,

x = 39/4

 If you want a decimal answer, if you did 39 divided by 4 by hand, you'd get 9.75. Both of these are the correct answer.

(Note: You'll get some questions that actually tell you what form they want the answer in. So, if they told you to write your answer to a specific number of decimal places, make sure you use the decimal answer, and also round it to the correct number of decimal places.

If you have any further questions, don't hesitate to contact me.

I am assuming you meant: (4/3)X-102/3+21=0

this is an algebra question.

to solve it,lets get rid of the fractions. since 3 is in the denominator, we have to multiply both sides by 3. this gives us:

(4/3)*3*X -(102/3)*3 + 21*3= 0*3

next we get this by simplifying:

4*X -102+63=0

lets make X the subject. add -102 and 63 to get: 63-102= -39

the equation looks like this: 4*X -39=0

hence add +39 to both left and right side, we get this: 4*X +39 -39 = 39

lastly divide each side by 4, to get 1 as the coefficient of X:

answer :           X=39/4 or 9.75

I suppose you mean 4X/3-102/3+21=0. The first thing you need to do is get rid of the fractions by multiplying all terms by 3. This gives you

4X-102+63=0. Next step: get rid of all the numbers on the left side and leave only 4X over there. This gives you 4X=102-63

4X=39 Divide my the coefficient of X (the number in front of X)

X=39/4 which is a fraction at its simplest form. Please let me know if you hadn't written down correctly the equation that you had. If that as it, this is your answer :-)

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