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I have finished the essay. If you hand in this essay as is, it is plagiarism. You will need to format it as well. There is plenty of time for you to read the essay, learn how to do these equations and rewrite it in your own words. In future, please give tutors more time than one day to write a 3000 word essay, especially when the essay is due more than a month away.
Algebraic equations allow people to solve for quantities that are not known. Many times it is not
possible to directly figure out how much something is through a measurement alone. You might also
want to predict what something is without building everything necessary to find out. If you know, for
example that something costs $10, and you want to know how many you could buy with $500, you can
set up an equation, 10X = 500. Ten represents the rate, and X represents the unknown. To solve any
equation, mathematicians use various methods to use known information to find unknown information.
They set up the information in a number sentence, and then do inverse operations to isolate the
unknown. This essay will talk about how to solve the three most common types of single variable
equations: linear equations, quadratic equations, and exponential equations.
All equations are built out of quantities and variables. Variables are unknown so they cannot be
represented by exact numbers. Unknowns are usually represented by the letter X but it helps the person
solving the equation if they use letters that hint at the answers. For example, if you were trying to solve
for how many Widgets are going to be needed, the variable could be written as W. They are called
equations because one quantity, also known as an expression, is equivalent to another expression. If for
example we say that six cereal boxes cost forty-two dollars, we could write this as an equation: 6C = 42.
The unknown, C, denotes the price of the Cereal box. It is obvious that six times whatever the price is is
equivalent to the total 42. So both expressions are placed at opposite sides of the equal sign. Whenever
steps are taken to solve any equation, whatever is done to one side of the equation must be done to the
other side in exactly the same way. If this does not happen, the equivalent relationship between the two
expressions will be changed. For example, if you added 5 to one side and not the other, you would get
6C = 47. The expression would then say they price of six cereal Boxes is forty-seven dollars instead of
forty-two. This would be a different problem. If you added 5 to both sides of the equation, you would
get 6C + 5 = 47, which is differently phrased but still expresses the same relationship as before. Five
more than the 6 boxes of cereal is five more than forty-two, or forty seven.
For this reason, when one is to solve an equation, one must do the same operations to both sides of the
equation in order to isolate the variable. If this is done, the equivalence and the expression is
maintained. The complexity is simplified. Let us solve the equation already discussed as an example: 6C
+ 5 = 47. The C value on the right needs to be isolated so that the value can be determined. There is a 6
and a 5 on that side that must be removed. It would change the relationship if one just crossed them
out. The first thing one should do is subtract the five on both sides. This helps isolate the variable. 6C + 5
– 5 = 47 – 5. Numbers go with numbers and variable expressions go with variable expressions that are
like them. This is called combining like terms and must be done so that equations become easy to solve.
The...