Solving Equations

In the equation x - 4 = 6, we are trying to find out what x equals. In order to do this, we need to get x all by itself and everything else on the other side of the equation. We take it one step at a time and use these rules as a guide:

Remember:
1. The order of operations must always be observed.
2. Work with the numbers furthest away from x first.
3. To get rid of a number from one side, do the opposite of what is being done to it.
4. Whatever you do to one side, you must do the same thing to the other side.

Examples:

x - 4 = 6

  + 4   + 4        Add a 4 to each side to get rid of the - 4 on the left side of the equation.

x = 10             The 4 is gone from the left side of the equation. 6 + 4 = 10, so x equals 10.



Let's try another example.  Use the same rules listed above.

2x + 3 = 15

   - 3   - 3       Subtract a 3 from each side to get rid of the + 3 on the left side.

2x = 12            The 3 is gone from the left side. 15 - 3 = 12, so 2x equals 12.

--   --

2     2            Divide both sides by 2 to get rid of the 2 on the left side. 2x means 2 times x.

x = 6              The 2 is gone from the left side. 12/2 = 6, so x equals 6.

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Other Links

Get Math Homework Help from the Discovery School web page.

Go to the Math Forum at Swarthmore College.

Go to the SCORE Math page by the Kings County Office of Education.

See the California Mathematics Academic Standards for K - 12.