You may want to review arithmetic with fractions, simplifying expressions and the idea of equations first.

Solving an equation means working out what *x* needs to be
in order for it to be right. This is one thing that teachers
generally cover pretty carefully, so I won't say as much. Briefly,
you want to turn your equation into another equation that says the
same thing, but with *x* all by itself on one side and a
number on the other side. For the sorts of equations you'll see at
this point, here are the steps:

- Simplify both sides. For example, if you were given 5
*x*+ 2 = 3(*x*− 1), you could simplify the right-hand side. You would get 5*x*+ 2 = 3*x*− 3. (The left-hand side is already simplified.) - If there's an
*x*on both sides, fix that. You can do that by adding or subtracting the same thing from both sides. For example, if you have 5*x*+ 2 = 3*x*− 3, you can subtract 3*x*from both sides, getting 2*x*+ 2 = −3. If*x*is only on one side, you can skip this step. - If there's a number being added or subtracted on the side
where the
*x*is, subtract or add it from or to both sides so it won't be there any more. In the example above, you would subtract 2 from both sides, getting 2*x*= −5. If there's no number being added or subtracted, you can skip this step. - If there's a number being multiplied by the
*x*, divide both sides by it. In the example above, you would divide both sides by 2, getting*x*= −5 ⁄ 2. This means the only solution is −5 ⁄ 2. If*x*is already by itself, you can skip this step.

Remember, −*x* is the same thing as
(−1)*x*. So, for the last step, if you have
−*x* on one side, you can divide both sides by
−1.

Fractions are just a kind of number. So if there are fractions anywhere in the equation, you just need to treat them like any other number. (This means you need to remember how to do arithmetic with fractions.)

One funny thing that can happen is that the *x* can
disappear (or never have been there to begin with). In that case,
the equation is either right (no matter what *x* is) or wrong
(no matter what *x* is). If the equation is always right,
then we call it an *identity*. If it's always wrong, then
we call it a *contradiction*. Otherwise (that is, if
there's a single number that *x* has to be), we call it
a *conditional equation*.