Elementary equation and inequality review

If you've never seen equations before, you need to see this page before going any further!!!

Given an equation, e.g. x + 2 = 5, you typically want to solve for a certain variable within the equation (in this case, x). In order to do this, you can perform mathematical operations to both sides of the equation to get the desired variable by itself. In the above equation, if you subtract 2 from both sides, you get x + 0, which is just x, on the left-hand side and 5-2, or 3 on the right-hand side. Therefore, x = 3.

Notice that if you put 3 back into your original equation, we obtain 3 + 2 = 5, which is in fact a true statement. Therefore, x = 3 is a solution to the equation x + 2 = 5.

Now, let's look at another scenario. What if we had the equation 3x = 9? By now, you should know that a number and a letter placed side by side means that they are multiplied. Then, the above equation should read, "3 times x equals 9, or simply, 3x equals 9." In order to isolate x on the left-hand side, what should we do? If you said, " multiply both sides of the equation by the multiplicative inverse of 3", then you are correct. Multiplying both sides by 1/3 gives us x = 3. Substituting 3 back into our equation, gives us 3*3 = 9, which is indeed true! Therefore, x = 3 is a solution of 3x = 9.

Inequalities work the same way, but with one minor difference... Return to Day Seven to find out.