Solve equations with more than one variable, Algebra

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Solve   A= P (1 + rt ) for r.

Solution

Here is an expression in the form,

                            r = Equation involving numbers, A, P, and t

In other terms, the only place which we want to see an r is on the left side of the equal sign all by itself. There must be no other r's anywhere within the equation. The procedure given above must do that for us.

We don't have any fractions hence we don't have to worry about that. To simplify this equation we will multiply the P through the parenthesis.  Doing this gives,

                                                          A = P + Prt

Now, we have to get all the terms along an r on them on one side. This equation has that set up already for us that are nice. Next, we have to get all terms which don't have an r in them to the other side. It means subtracting a P from both sides.

                                                             A - P = Prt

As a last step we will divide both sides through the coefficient of r.  Also, as noted in the procedure listed above the "coefficient" is not a number.  In this particular case it is Pt.  At this stage the coefficient of variable is only all the stuff that multiplies the variable.

A - P/ Pt = r            ⇒            r = A - P /Pt   

To get a last answer we went ahead & flipped the order to get the answer in a more "standard" form.

We will work more examples within a bit.  Though, let's note a couple things first. These problems tend to appear fairly hard at first, however if you think about it all we really did was use exactly the similar procedure we used to solve linear equations. The major difference of course, is that there is more "mess" in this procedure.  That brings us to the second point.  Do not get excited regarding the mess in these problems.  The problems will, on occasion, be a little messy, however the steps involved are steps that you can do! At last, the answer will not be a simple number, however again it will be a little messy, frequently messier than the original equation. That is okay & expected.


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