7. Solve for x and check
First we need to clear denominators. Multiply both sides by c.
Transpose known terms to one side and unknown terms to the
other. The simplest way to get all of the x terms together on the
same side of the equation would be to transpose the ax to the right.
To get the x's altogether in one place, factor an x out of the two
terms on the left side of the equation.
Now, we need only divide both sides by the coefficient of x.
If a = c, then we will have a zero denominator, and the
expression will not give us a solution. In this case, if b = 0, then so
long as c is not 0 any value of x will give us a solution. Otherwise,
there will be no real solution.
Copy down the original equation
except, where you see an x, substitute the solution in parentheses.
On the top of the left side we are adding fractions, so we need
to find common denominators.
Now that we have common denominators on the top of the
right, we can add the fractions.
this simplifies to
If we invert and multiply, we get
and it checks.
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