3. Solve for   x   and check

First we need to clear denominators. Multiply both sides by   c.

ax + b = cx

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.

b = bx - cx

To get the x's altogether in one place, factor an   x   out of the two terms on the left side of the equation.

b = (c - a)x

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.


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


and it checks.

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