# Chapter 6: Rationals: Multiplication, Division, and Applications

by

Millard Lewis and John Moore

## Day 9: Two-Step Equations

This lesson should use many of the ideas that we've discussed throughout the last eight days. Recall that in Day 7 we discussed solving equations and inequalities using rational numbers. The concept of solving two-steps equations is very similar to that, but it simply involves one more step...

If we had the equation x + 5 = 6, we solved this by subtracting 5 from both sides in order to keep our equation balanced and to get the variable (x, in this case) by itself. This results in x = 1. We also stressed the importance of checking our answer to make sure that we did not make a mistake. Doing this, we see that 1 + 5 = 6, and this is true! So, we must have performed the correct operation!

Now let's look at a two-step equation. How about 5x + 3 = 13? The first thing that we need to do is begin to isolate the x. Start doing this by combining the like terms, or, in this case, subtract 3 from both sides. This leaves 5x = 10. Well, we've seen equations like this before! Multiply both sides by the multiplicative inverse of 5, or 1/5, and we obtain x = 2. Checking our answer, we find that 5*2+3 = 13. This turns out to be true!

Now let's try some examples! Activity: If you have access to Algebra Xpresser, try to graph your homework problems. Most (if not all) of the graphs will be vertical lines. BUT, where these lines cross the x-axis this the solution to the equation. Why does this happen? What else can graphs tell us in mathematics?