3.5+Solving+for+X

Section 3.5 - Solving for X
Earlier in this chapter we had simple equations that included a variable and it was relatively easy to figure out what the variable had to be in order to make the equation true. ( 3w = 4 + 8)

However as the equations get more complex (just wait for fractions and decimals), there is a set of three steps that can be used to solve any of these single variable equations. Sometimes you won't need all three steps, but there are only three, they go in a certain order, and they always work, unless there isn't a solution that could make the equation true.


 * Step 1 - Simplify Each Side of the Equation **

Combining like terms means adding or subtracting "like terms", as long as they are on the same side of the equals sign.

A quick review of the Distributive Property: 3( y + 4 ) = 3y + 12

This simplifying happens on each side of the equals sign, if possible. Sometimes it won't be necessary to simplify one or both sides.


 * Step 2 - Isolate the Variable **

This is the official phrase. A more accurate one would be to segregate the constants (numbers) and the variables (with their coefficients). Get the numbers on one side (either side) and the letters on the other. Sometimes we talk about "moving" the constants or the variables from one side to the other, and it does kind of seem that it works that way, but a more accurate way to describe it would be that you are adding or subtracting the same amount on both sides of the equals sign in order to "cancel out" one of the terms.




 * Step 3 - Divide Both Sides by the Coefficient **

The last step is to divide both sides by the coefficient in front of the variable. This will a single variable ( such as 1x ) and that is the answer.



Do not leave the variable negative. If you end up with something like - x = 4, multiply or divide both sides by -1. You would get x = - 4 in this example.

The easier equations: media type="youtube" key="VidnbCEOGdg" height="390" width="640"

All the steps together: media type="youtube" key="CGS0vihzSlc" height="390" width="640"

media type="file" key="balloon of fire.flv"


 * Chapter Three Practice**

**Where to from here?**
3.1 Variables and Constants 3.2 Terms 3.3 Equations 3.4 Formulas 3.5 Solving for X 3.6 Two Unknown Relative Values Chapter Three Summary Chapter Three Homework