Confused about the steps/rules for rearranging equations?

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In summary, the student needs to be doing the exercises, as well as studying from other resources (like Schaum's Outlines). Drawing pictures and graphs can be helpful in solving equations and inequalities.
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Homework Statement


Hi guys,
Sorry in advance for posting this type of question in this section as I'm sure it belongs somewhere else, however it technically still is homework for me as I'd really like to be able to get good at this. Personally I've never been great at rearranging equations to solve for any given variable and id just like to know what exactly the steps/rules are (BEDMAS?) when you look at a certain equation and you want to know exactly what to do first? Due to poor teachers in the past few years my basic algebra skill isn't very good and I'd really like to improve it if at all possible. Therefore if any of you guys could give me some insight on what steps to do first when tackling a problem, or could link me a really good resource on this topic I would really appreciate it.
Thanks

Homework Equations


For example in my math course there is a formula for compound interest: A=P(1+i)^n and I have to solve for n. I just wouldn't know how to really do this.

The Attempt at a Solution


A=P(1+i)^n
A/P=(1+i)^n - Are you even allowed to do this first??
ln(A/P)=n(ln(1+i))
n=ln(A/P)/ln(1+i)
Can someone tell me if this is correct or terribly wrong?
Thanks
 
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  • #2
It is correct. Well done. Now create a notebook and label it "Bag of tricks". Add this as a trick to solve for an unknown exponent.
newguy_13 said:
Are you even allowed to do this first??
You are allowed to divide both sides by P as long as P is not zero. But then A would also have to be zero and your starting equation is 0 = 0. OK, let's do something more interesting.
 
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To add to what @kuruman said, you are allowed to perform any arithmetic operation (except division by zero) to both sides of the equation, resulting in a new equation whose solutions are the same as the original equation. This is why it was valid to divide both sides by P, as you did. You can also apply any function to both sides, provided that the expression on each side is in the domain of the function being applied, although some functions (like squaring both sides) can result in extraneous solutions). This is why it was valid to take the log of both sides -- presumably A/P is positive, and since 1 + i > 1, ln(1 + i) is also positive.
 
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Thanks guys!
Anyone know of any resources that would help my algebra skill?
 
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newguy_13 said:
Thanks guys!
Guys and Gals. Some of our best homework helpers are female. :smile:

One other suggestion to add to the good advice you've gotten so far in this thread... In physics type problems (as opposed to pure math problems), carry units along in the equations as you work through them. The units should be the same on both sides of the "=" sign, and should be the same for any quantities that you add or subtract. Carrying units along in your equations helps you to catch algebra mistakes in larger computations, and helps you to sanity check your work at each step. If you end up with units like [m^2/s^2] = [m/s^2] at some point, you can see right away that you need to look back to figure out which term you dropped... :smile:
 
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To solve for a variable, you do the reverse operations and reverse order that you would do to evaluate that side. You are trying to strip away the operations one-by-one till you are left only with the variable of interest.
 
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newguy_13 said:
Thanks guys!
Anyone know of any resources that would help my algebra skill?

Try "Schaum's Outline of Elementary Algebra". It is under $20, and before buying you can download a limited-time free pdf version which you can examine for appropriateness. The Schaum's books are loaded with hundreds (sometimes thousands) of solved problems showing step-by-step the procedures involved. You can also get Shaum's Outlines of College algebra plus numerous other relevant subjects. Google "Schaum's Outlines".
 
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I clicked on "Like" for the posts here which are in my opinion, most helpful. Not that the other posts are not helpful, just that what I put "Like" to are maybe the best up to now.

Student needs some experience at Algebra and equation & inequality solving.

Algebra course/courses are for learning the rules which govern arithmetic. They become, with study and PRACTICE, like a language in which to think. You usually do not see all the steps in your head all at once; but should be able to pick each step one at a time.

Do all of your assigned exercises. Do maybe more than just the assigned exercises. Sometimes you might benefit from checking and studying from another book.

Draw pictures and draw graphs. This can OFTEN help. Use a number line. Not always what you need, but at times, this helps very much. There are students who refuse to draw figures, graphs, diagrams. Such students restrict their own learning very badly.

You will hopefully, find some reasons or ways to use some algebra, outside of just your Algebra 1&2 & College Algebra courses. Some hobby activities can give opportunities for algebra. Some consumer activity may, too. Obviously, Physics, Chemistry, and any kind of Engineering have plenty opportunity for using Algebra and other Mathematics.
 
  • #9
newguy_13 said:
Thanks guys!
Anyone know of any resources that would help my algebra skill?
Textbook on Intermediate Algebra
and some textbooks on College Algebra

Amost ANY such books, even if they are several or more years old.
 

1. How do I know which step to perform first when rearranging an equation?

When rearranging equations, it is important to follow the PEMDAS order of operations. This stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). So, you should start by simplifying any parentheses or exponents, then move on to multiplication and division, followed by addition and subtraction.

2. Can I change the order of the terms on both sides of the equation when rearranging?

Yes, you can rearrange the terms on both sides of the equation as long as you perform the same operation to both sides. For example, if you want to move a term from the right side to the left side, you can subtract it from both sides. This will maintain the equality of the equation.

3. What should I do with fractions when rearranging equations?

When dealing with fractions in equations, it is helpful to multiply both sides of the equation by the denominator of the fraction to eliminate it. This will allow you to work with whole numbers and simplify the equation.

4. Is it necessary to show all the steps when rearranging equations?

It is a good practice to show all the steps when rearranging equations, especially when working on more complex problems. This will help you keep track of your work and avoid making errors. It also makes it easier for others to follow your reasoning and understand your solution.

5. Can I use different methods to rearrange equations?

Yes, there are multiple methods you can use to rearrange equations, depending on the specific equation and your personal preference. Some common methods include moving terms from one side to the other, factoring, and using inverse operations. It is important to choose a method that works best for you and helps you arrive at the correct solution.

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