Ho do i solve lieral equations?

Algebra
Tutor: None Selected Time limit: 1 Day

I need help with literal equations because i don't understand how you can solve an equation with letter. I don't understand the process of multiplying,dividing,adding and subtracting letters.

Sep 9th, 2015

Thank you for giving me the chance to help you out!

Literal equations are best attempted only after you understand how to do regular equations with one variable. I'm going to quickly show you step by step how to do one of those before showing you that it is the exact same process with letters (which represent numbers!)

Say we have the equation....

(2x+5) / 3 = 5

You always want to get some kind of variable alone on one side of the equation. Remember, to keep the equation the same, anything we do to one side will need to also be done to the other. You may wonder where to start. The trick to this (that most teachers do not share with you) is to get rid of what's furthest away from x on one side of the equation first.

In this example the 2 is really close to the x so that cannot be where we start. The +5 is also fairly close by in the same parentheses. The number furthest away from x on that side of the equation is the divided by 3. To cancel anything on one side of the equation, you do the opposite of it to both sides. You cancel a divided by 3 by multiplying by 3 to both sides. On the left side of the equation the 3's will cancel out. On the right side you will have 5 * 3=15 and the equation should look like this

(2x+5)=15

Then you cancel the next furthest thing from x on the same side of the equation which is the add by 5. Cancel out add by 5 by subtracting both sides by 5. You will get

2x=10

Finally, when two numbers are together like 2 and x that is understand to mean multiply. A multiply by 2 is the last thing we need to cancel that is with x by doing the opposite to both sides of the equation. The opposite of multiply by 2 is divide by 2 so do that to both sides to get the final answer.

x=5

It is the EXACT same concept with doing literal equations.

Say for example we have the interest formula

i = prt

You are told to solve the equation for letter t. Well, you now know that you  are trying to get t alone on one side of the equation by first cancelling the other numbers that are around it out by doing the opposite. Normally, you start with the number (letters in this case) furthest from what you are trying to get alone but both the p and the r are equal so pick either. Let's start with the r. Since r is right next to t (just like the 2x in the example above) that means its multiplying. The only way to cancel out a multiply by r is to divide by r to both sides of the equation. You are left with

i / r = pt

Now cancel out the p. Again p is multiplying by t so the only way to cancel it is to divide by p on both sides of the equation. You should get as your final answer

i / rt = t


I hope this was helpful! Please let me know if you need any further help or clarification
Sep 9th, 2015

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Sep 9th, 2015
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Sep 9th, 2015
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