33-2x=5-9x

Your goal is to get x all alone.

Even i had trouble and still do with these equations, but every time you get rid of something you have to think of the consequences that's why you should take away the small things so that the equations is closer to x and its less complicated.

In the coding, i have shown what i added or took away.

Look at that and speak to me after if you're still having trouble answering it.

When i added 9x if instead +2x i would have gotten a negative but it's still right and i still would have gotten an answer.

$$\begin{array}{rrl} 33-2x&=&5-9x\qquad(- 5)\\ 28-2x&=&-9x\qquad(+2x)\\ 28&=&-7x\qquad(28\div(-7)=-4)\\ x&=&-4\\ \end{array}$$

Also correct!

$$\begin{array}{rrlll}33-2x&=&5-9x\qquad&(- 5)\\ 28-2x&=&-9x\qquad&(+9x)\\ 28+7x&=&0\qquad&(which\;means)\\ 28&=&-7x\qquad&(28\div-7=4)\\ x&=&-4\\ \end{array}$$

Hi MG

Your understanding of equations and your LaTex presentations are coming along brilliantly.

All the adults on the forum a are very pleased that you are learning here with us!

Your first post here was incorrect (you did not add 9x correctly) and you have redone it so you should delete your first post so it will not be confusing.

Better comments for the correct post would have been  

(-5 from both sides)

(+2x to both sides)

(divide both sides by -7)

Thanks Melody, but why was it wrong to + 9x

How did you know that it was wrong and you had to add 2x?

When you add 9x to both sides MG you should get 28 + 7x = 0, not 28 = 7x

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I know that Alan, but i just skipped it or is that part vital for the equation?

In that case, in your first answer you got a sign wrong when you skipped it!

28+ 7x = 0 isn't the same as 28 = 7x, it's the same as 28 = -7x

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I've edited my post. :) 

Thanks Melody and Alan!

It needs a further edit MG!  28 + 7x means 28 = minus 7x 

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Huh I'm not sure whether you mean negative 7x as its placed there or the operation sign minus?

I mean the fourth line of your first solution should look the same as the third line of your second solution.

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Ok, I'll do that but how does it turn from a positive to a negative number?

(Answer then is also -4)