Algebra Help: Solving for a Given Variable

Help with Algebra

Equations and Variables

Equations have two values or expressions on opposite sides of an equals sign. An equation is true when both sides are equal. Here are some examples:

5 = 5

5 = 3 + 2

1 + 4 = 3 + 2

Any number in an equation can be represented by a variable. For example, 3 + 2 = 5 could be written as 3 + 2 = x, 3 + x = 5 or x + 2 = 5. In beginning algebra, you'll be asked to 'solve for' variables in single-variable equations like these. Solving for a variable means figuring out what number the variable represents to make the equation true.

The good news is you've been solving for variables since you started learning to add. The problem 3 + 2 = ? is an equation, and the question mark is like a variable. The only difference is that, in algebra, the question mark is replaced by a letter, like x, and the solution is written as an equation, like this: x = 5.

However, most of the equations you solve in algebra will have the variable in a different place. For instance, you might be asked to solve this equation: 3 + x = 5. Since 3 + 2 = 5, x = 2. For the equation x + 2 = 5, x = 3 because 3 + 2 = 5.

Solving Equations

Often, you'll be asked to solve algebraic equations that are a little more complex. For instance, you might not be able to solve the equation 482 = x + 221 just by looking at it. To solve an equation like this, you need to isolate the variable, which means you'll have to manipulate the equation so that the variable is on one side of the equals sign by itself.

You can perform whatever operations you need to in order to isolate the variable, as long as you perform the same operation on both sides of the equation. For instance, if you add an amount to one side of the equation, you must add it to the other side as well. As long as you perform the same operations on both sides, the equation will remain true (both sides will still be equal).

To illustrate, let's say you want to solve the equation from earlier, 482 = x + 221. You want to get the variable, x, on one side by itself, and you can do that by subtracting 221 from the side with the x. For the equation to remain true, though, you need to subtract 221 from both sides, like this:

482 = x + 221

482 - 221 = x + 221 - 221

261 = x