In this section you can work algebra problems in which the variable, x, is in the denominator of a fraction. It's important to know how to do these. One very clear rule of algebra is

Here's an example of such a problem:

$$\frac{3}{x} - 4 = 11$$

As usual, the first step to solving such a problem is to do the easy stuff first, namely, move the -4 to the right by adding it to both sides:

$$ \begin{align} &\frac{3}{x} - 4 = 11 \\ &\underline{\phantom{00} + 4 \; + 4} \\ &\phantom{000}\frac{3}{x} = 15 \end{align}$$

Now we need to get the x out of the denominator. We do this my multiplying by x on both sides of the equation:

$$3 = 15x$$

Now dividing by 15 gets the x by itself, and we have

$$x = \frac{3}{15} = \bf \frac{1}{5}.$$

Another way to think about that last step is by cross-multiplication. If we write

$$\frac{3}{x} = 15 \; \; \color{#E90F89}{\text{ as }} \; \; \frac{3}{x} = \frac{15}{1},$$

we can cross multiply

to get $15x = 3,$ and so on.

You can practice problems of this type below. Follow the steps in the example and enter your answer as an integer or a fraction of integers, like 3/4, or a decimal number like 1.55 (if you must). Do as many problems as you need to get good at these. You'll form a solid foundation for what comes next.

Next we'll do some of these in which the integers are fractions. Everybody needs practice with fractions!

In this section, we'll refer often to **inverse** operations. Inverse operations are opposite, and one can be used to *undo* the action of the other.

**Addition**and**subtraction**are inverse operations.**Multiplication**and**division**are inverse operations.

There are a number of these pages you can use for algebra practice. Just pick the rough type of problem you need to work on.

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