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Math
A |
Solving
Equations |
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Solving
equations is just a matter of undoing operations that are being
done to the variable. |
In
a simple equation, this may mean that we only have to undo one operation, as in
the following example.
| Solve
the following equation for x: x + 3 = 8 |
The
variable is x.
We are adding 3 to the variable,
so to get rid of the added 3, we do the
opposite----subtract 3. (Remember
to
do this to both
sides of the equation) |
x + 3 = 8
-3
-3
x
= 5 |
In
an equation which has more than one operation, we have to undo the
operations in the correct order. First, undo addition or
subtraction, then undo multiplication or division.
| Solve
the following equation for x: 5x - 2 = 13 |
The
variable is x.
We are multiplying it by 5,
and subtracting 2.
First, undo the subtraction by adding 2.
Then, undo the multiplication by
dividing by 5.
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5x - 2 = 13
+2
+2
5x = 15
x = 3 |
Suppose
there are variables on both sides of the equation. The trick now,
is to get the variables on the same
side by adding them or subtracting them.
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Solve
the following equation for x:
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We
have two terms with the variable, 4x and x.
We'll
move the variable with the smaller coefficient, x.
To do this we have to look at the sign in
front
of the variable we're moving. Since there is no sign, we
know it is +.
To move this variable we do the opposite, so we'll subtract x from
both sides.
Now
we proceed as before.
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4x
+ 5 = x - 4
-x
-x
3x
+ 5 = -4 |
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3x
+ 5 = -4
-5 -5
3x = -9
x = -3 |
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