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The goal of algebraic equations is to find the number or set
of numbers which makes the equation true. Sometimes the answer can
be simple, other times it can be very complex, so we need to have a
process that allows us to find and answer which is correct.
This process is aiming to get the letter on the left hand side of
the equation by itself. To do this we must balance whatever we do to
one side of the equation with the other. So for example if you add 4
to one side of an equation you must also add four to the other.
Example
Let’s look at some examples:
Solve this equation: x + 7 = 12
Remember we want to isolate the x on one side of the
equation. So on the left hand side we get x and on the right we
get 12 minus 7. You final answer will be x equals 5. Here are
what the steps look like:
x + 7 – 7 = 12 - 7
x = 5
To check your work all you have to do is substitute your
answer back into the original equation for x.
5 + 7 = 12
Example
Let’s try this one:
Solve the following: 12x = 96
Lets start by thinking about what we are trying to answer. In
this case we want to know what number times 12 will equal 96.
You might be able to figure this out in your head, but let’s go
through the steps anyway.
12x = 96
 X = 8
Now let’s check our work. 12 x 8 = 96 is correct so we
have done this problem correctly.
Example
Let’ try one more!
Solve for X: 6 – (x + 3) = 10x
First we should expand our bracket by multiplying everything
inside the bracket by negative 1.
6 – x – 3 = 10x
Next we need to decide which side of the equals sign we are
going to isolate the x on. In this case it is easier to get all
the x’s on the right hand side. To do this we need to add 1 x to
each side;
6 – x – 3 + x = 10x + x
Notice the x’s on the left will cancel each other out and we
will be left with the following:
6 – (-3) = 11x
9 = 11x
Next we have to divide each side by 11.
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= |
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X= |
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or x = 0.8181… |
In some cases it might be possible that there are no possible
solutions to the equation or the solutions do not make since. There
for it is important to always check your solutions. |
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