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How to Do Algebra

February 19, 2012 | Comments: 0 | Views: 152

Algebra can be a tough subject for anyone, but understanding one simple concept can change everything. If you truly understand what equals means, you can suddenly do algebra.

As a tutor of many dozens of people, I have found that many want to ask if they should subtract 5, or divide by 3. If they understood the concept of equals, these would not be questions. When you are doing algebra, the only purpose is determine what the variable value is, usually denoted by an x. So you could have:


Now since we want to find out what x equals, we have to get it by itself, but to do so, we must make changes to the equation so that we get x=something.

However, we can do anything to the equation as long as we do it to both sides of the equation. This is because = means that the two sides of the equation do not have to look the same, but they are the same value. So whatever 2x+5 is, it is the same as 17. We just have to figure out which value of x makes that true. So we could start by getting the 2x by itself by subtracting 5, but don't forget, to make it equal, we have to do it to both sides.

2x+5=17 -5 -5 2x=12

Now we know that 2 x's are equal to 12. So if divide by 2, we will have x by itself.

2x=12 2 2


So now we have the answer. To get it, everything we did was done to both sides of the equation. Now, to clarify, if you are doing division of multiplication, it has to be done to all of the values on both sides. So let's say we have the following equation:

2x+3=7x-7 2 2 2

A good thing to do here would be to multiply by 2 so we don't have to deal with fractions, but again, we have to do it to everything on both sides, so we get:

2x(2)+3(2)=7x(2)-7(2) 2 2 2 which is the same as


So even though the 2x did not need to be multiplied by anything because it wasn't a fraction to start with, we still had to multiply it by 2 because we were doing it to both sides of the equation.

One way to think of equals is like a scale that you are trying to keep balanced. Let's say you have 10 lbs. on each side of the scale so that it is perfectly balanced, or equal. Now if we removed 1 lb. from one side, the scale would no longer be equal until we did it again to the other side. If we divided the weight on one side by 2, then we would have to do the same to the other to keep it balanced.

So remember, if you want to know how to do algebra, all you have to do is understand that equals means that the two sides have the same value, so everything you do to one side must be done to the other.


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