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.

Check

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.

Remove parentheses.

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

or

and it checks.

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