Question 118508: Iam the mother of a 13 year old that is having troubling with algebra and I really need to understand how the solutions are found in order to help him.
Example: 5x + 7 -2x = 22
Answer by tutor_paul(519)   (Show Source):
You can put this solution on YOUR website! 
I assume the problem is to "solve for x?" If so, this is how you generally do problems like this.
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The first step is to get all the terms with x in them on one side of the equation, and everything else on the other side. In this case, you already have the 5x term and the -2x term on the left. That's good. You need adjust the equation so that 7 is not on the left side of the equals sign.
How? Well, remember that equals sign means something, and you need to maintain that equality. So whatever mathematical thing you do to one side of the equation, you need to do the exact same thing to the other side in order to keep that equals sign valid. So, if I want to get rid of that 7 on the left, I need to add a -7 to it. That works since 7-7=0, and voila, the 7 is history. However, like I said, you better do the same thing (add a -7) to the right side to maintain the equality. So you now have this:
See how I added that -7 to both sides?
Now, you can simplify this a bit by combining the integers:
Next, since 2x and 5x are "like terms," i.e. they are both x terms, they also can be combined:
You are almost done... however you need x alone on the left. So you need to get rid of that coefficient of 3. How?
Notice 3 is multiplying the x. Like before, you need to apply the inverse operation (division) to get rid of that 3. So, again keeping the equality, divide both sides of the equation by 3 to get x alone.
Notice this is a legal operation since I did it to both sides of the equation. Now, you know that
 , therefore, you will be left with just x on the left (that was your goal!). Just simplify the right side and you are done!
Good Luck,
tutor_paul@yahoo.com
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