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Lesson 106a: Intro to Algebra (Part 2)
In this lesson, you'll learn how to use algebra to solve equations with different type of operations: addition, multiplication, and division.
Be sure to first study Lesson 105. Take a look at this equation: x + 4 = 9. Our task is the find the value of x in this equation.
In this equation, it's very easy to figure out the answer. x is 5. You can do it in your head. But, if the numbers were more complicated, we would need a procedure to use. Here is what we do. We want to try to isolate x by itself on one side of the equal sign. Once it's by itself, it's value will be obvious.
What can we do to get x by itself? We need to see what is happening with the x. We're adding 4 to it. What is the opposite of adding 4 to a number? It's subtracting 4. Addition and subtraction are inverses of each other.
It's helpful to set up the equation like this:
x + 4 = 9
- 4 -4
---------
x = 5
You can see that the +4 and -4 cancel out. We're left with x = 5. It's very important to always check your answer, like we did in the previous lesson.
Look at the equation 3x = 18. Remember that we're now using x as a variable, and no longer as a multiplication sign. In this particular equation, though, we are multiplying, and we represent that with the absence of any symbol. This equation means 3 times x. As before, we can do this in our head. x is 6. But if the numbers were more complicated, we would need a procedure. Here is what we do.
What can we do to get x by itself? We can divide each side the of the equation by 3. Multiplication and division are inverse operations. Here is how we'll set it up:
3x = 18
-- --
3 3
The 3's cancel out. 3/3 equals 1. What we now have is 1x = 6. Whenever we have 1x, we just drop the 1, and write x by itself. We can see that x = 6.
Look at the equation x / 7 = 5. What is happening to the x? We're dividing it by 7. We can do the inverse to each side of the equation, which is to multiply by 7. Here is how we'll set it up.
x
- · 7 = 5 · 7
7
Be careful. On the left, we're really multiplying by 7 / 1, which we know is the same as 7. Since we have a 7 in both the numerator and the denominator, they cancel out, becoming 1. We now have 1x = 35, and we've seen that we just drop the 1 before the x. Our answer is x = 35. Remember to always check your answer in the original equation, and see if it works.
You'll have more practice with algebra in the upcoming lessons. Be sure to memorize the procedures shown in this lesson, and practice them.
Remember that you can ask a math question if you have additional questions about a topic, or you can contact me if you have any comments or suggestions for this site.