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-5 = 2x + 5

I want to "re-start" my mathematical education. I am needing it more and more at work. A co-worker asked me to break that down (he couldn't remember either).

Where should I start? What books?

Thanks!

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3 Answers 3

up vote 13 down vote accepted

This is an equation, because it says "Left hand side = Right hand side".

Think ow an equation as a scale in perfect balance. Now you have to rearrange everything, without destroying the balance, so that the $x$ will appear at one side alone. Because then you know what $x$ is.

For example, if you take away the same amount from both sides, the scale will remain in balance. So, let us take away $5$ from both sides, and we end up with

$-10 = 2x$

Now, if the scale is in balance now, it will remain in balance when we make each side half as big, because if two things are equal, then their halves are equal as well. This leaves us with

$-5 = x$

The scale is in balance, on the left side we have a $-5$ and on the right side we have $x$. Therefore, $x$ has to be $-5$.

Now, to re-start your education: The problem above is elementary algebra, so I'd pick up with an algebra book that starts from the beginning. Something like "Math for Dummies" might be a nice idea as they are fun to read.

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@cbmeeks: And a good habit is that once you think you've found the right value of $x$, you put it back into the equation that you started with in order to see that the equation really is satisfied. In your case, the "$2x+5$" on the right-hand side becomes $2 \cdot (-5)+5$ when you let $x=-5$, and this expression simplifies to $-5$. Thus the right-hand side agrees with the "$-5$" that you had on the left-hand side, so we have verified that our solution $x$ indeed is a solution. –  Hans Lundmark Dec 2 '10 at 19:03
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Hint: In general for such one variable problems, where you need to find the value of the variable from a given single equation, you collect terms in the variable on one side of the equation and terms not containing the variable on the other side. Then divide the equation by the coefficient of the variable ($x$ in this case) to solve for it.

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This is elementary algebra, there are Schaum's books on that.

Anyway, you solve for $x$ like this:

$-5 - 5 = 2x + 5 - 5$ (substract 5 from each side), this gives $-10 = 2x$. Now divide both sides by $2$ to get $-10/2 = 2x/2$ so $x = -5$.

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