Solve This Equation
Solve This Equation
This sections il ustrates the process of solving equations of various forms. It also shows you
how to check your answer three different ways: algebraical y, graphical y, and using the
concept of equivalence.The fol owing table is a partial lists of typical equations.
SOLVING LINEAR EQUATIONS
Recall the following:
1. A linear equation is a polynomial of degree 1.
2. In order to solve for the unknown variable, you must isolate the variable
3. In the order of operations, multiplication and division are completed before addition and
subtraction.
"Linear" equations are equations with just a plain old variable like "x", rather than something
more complicated like x2 or x/y or square roots or such. Linear equations are the simplest
equations that you'll deal with. You've probably already solved linear equations; you just didn't
know it. Back in your early years, when you were learning addition, your teacher probably
gave you worksheets to complete that had exercises like the fol owing:
Know More About :- Linear Equations with Fractions


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Once you'd learned your addition facts well enough, you knew that you had to put a "2" in the
box. Solving equations works in much the same way, but now you have to figure out what
goes into the x, instead of what goes into the box. However, since you're older now, the
equations can be much more complicated, and therefore the methods you'l use to solve the
equations wil be a bit more advanced.
In general, to solve an equation for a given variable, you need to "undo" whatever has been
done to the variable. You do this in order to get the variable by itself; in technical terms, you
are "isolating" the variable. This results in "(variable) equals (some number)", where (some
number) is the answer they're looking for. For instance: Copyright (c) Elizabeth Stapel 2002-
2011 Al Rights Reserved
Solve x + 6 = -3
I want to get the x by itself; that is, I want to get "x" on one side of the "equals" sign, and some
number on the other side. Since I want just x on the one side, this means that I don't like the
"plus six" that's currently on the same side as the x. Since the 6 is added to the x, I need to
subtract to get rid of it. That is, I will need to subtract a 6 from the x in order to "undo" having
added a 6 to it.
This brings up the most important consideration with equations: No matter what kind of
equation you're dealing with -- linear or otherwise -- whatever you do to the one side, you
must do the exact same thing to the other side! Equations are like toddlers in this respect: You
have to be total y, totally fair!
Whatever you do to an equation,
do the S A M E thing
to B O T H sides of that equation!
Probably the best way to keep track of this subtraction of 6 from both sides is to format your
work this way:
Learn More :- Examples of Linear Equations


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What you see here is that I've subtracted 6 from both sides, drawn an "equals" bar underneath
both sides, and added down: x plus nothing is x, 6 minus 6 is zero, and -3 plus -6 is -9. The
solution is the last line of my work: x = -9.
The same "undo" procedure works for subtraction:
Solve x - 3 = -5
Since I want to get x by itself, I don't want the "-3" that's with the variable. The opposite of
subtraction is addition, so I'l undo the -3 by adding 3 to both sides, and then adding down:
Then the solution is x = -2.


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