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Equation Operations and The Golden Rule of Algebra

Here you will learn about how to solve algebra equations using simple steps and rules, along with how to enforce the Golden Rule into your problem-solving.

Victoria Huit

on 16 May 2010

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Transcript of Equation Operations and The Golden Rule of Algebra

What's the Golden Rule? How do we apply the Golden Rule? The Golden Rule states that what you do to one side of an equation, that side being
what is on one side of the equal sign, you must do to the other side. This is very important
to learn, especially before entering any algebra lessons. First it should be stated, that when solving for an unknown variable in an equation, you must try to get 0 on the side with the unknown variable in addition/subtraction (and get 1 in multiplication/division). This means, that you subtract/add (whatever the opposite is of whatever has been done) on the first side, and the second. In multiplication/division, it means that you are multiplying/dividing (whatever the opposite is of what has been done) on the first side, and the second. Even though you must know to do this on both sides, you must know why to do this to the overall expression that both expressions are equal to in the first place. You do it to cancel out any other number/operation to isolate the variable, which we'll talk about later.

For example, in the equation 4x + 39 = 51, your first step would be canceling out the 39 so that you can isolate 4x (this is the first step to 'isolating the variable', which is x). Therefore, the equation would now look like this, after also applying the Golden Rule.

4x + 39 - 39 = 51 - 39 = 12

Now we know that 4x = 12
Isolating the variable? Now, you've heard about isolating the variable before, but to make
sure you really know what it means, I'll remind you. When you are
isolating a variable, your are taking the other known variables in an
equation/problem, and manipulating them to get that one unknown answer
that you've been looking for.

Now, the next step to the equation stated before is isolating the variable.
How do you do that? Well, at this step in the equation we know what 4x
is (12). Now, we use this knowledge to 'isolate the variable', by dividing
4x by 4 because division is the oposite of multiplication, which is used
to multiply 4 and x.

4x/4 = 12/4 = 3
Now we know, because 4x = 12 that when you divide by 4 on both sides,
that the outcome will be x.

Therefore, x=3. What about multiplication/division? The steps in multiplication/divsion are basically the same. You use the oposites in the
same situations, but, you must remember that when you are doing the opposite to 1 side, it
is to get 1, not 0 like in addition/subtraction. Real life Applications Equations are all around you. When you're shopping, accounting, planning, and computing, you have to involve equations. For example, this sort of question could come up any day: What's the cost of a case of soda if you paid 32 dollars for 2 cases and tipped 4 dollars? That would create an equation that you would have to solve. The equation would be: 2x + 4 = 32. See? Equations are all around you, and learning how to solve them will help you in everyday life. Remember, that in order to
isolate the variable you have to
do the opposite to anything
with the variable so that it is
cancelled out. Bibliography HotMath. N.p., n.d. Web. 25 Apr. 2010. <http://www.hotmath.com>.
Siddiky, Zubair. Personal interview. 28 Apr. 2010.
Solving Equations
The Golden Rule of Algebra
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