One Step Algebra

Student: I do not understand the idea of solving for "x".

Mentor: Well, let's look at a specific problem where we have to solve for x:

Student: I just don't understand what the problem is asking me to do.

Mentor: Well, in this problem "x" represents a number. Since we don't know what the number is we are using a letter to stand in its place.

Student: OK, so I'm trying to find out what number "x" is representing?

Mentor: Yes, to do this we should think about the problem for a second. This problem is saying that if you add three to the unknown number ("x"), then you get 4. Do you know what that would mean "x" is?

Student: The number 4 is only one more than 3 so that means that "x" is 1.

Mentor: Lets check our work. We'll replace "x" with the number you just found that it represents. Is this number sentence true: 4 = (1) + 3?

Student: Yes!

Mentor: Let's look at a more complicated problem:

Student: I don't know what number you take 13 away from to get 22.

Mentor: Well for problems like this where the answer does not pop out at you, we try to get "x" on one side of the equals sign by itself to find the answer.

Student: What does that mean?

Mentor: On one side of the equals sign you will have the "x" (it can be either the right side or the left side) and on the other side of the equals sign you will have the numbers in the equation.

Student: How do you get "x" by itself? In this problem we would want to get the 13 away from the side with the "x" so that the "x" will be by itself.

Mentor: There is a number that we can add to the expression x - 13 to get rid of the 13. If we add 13 to the negative 13 then we would have x - 13 + 13. We get x + 0 which is just x.

Student: You can just add any number to the equation?

Mentor: You can add any number to one side of the equation as long as you add the same amount to the other side of the equation. You have to do the same thing to both sides in order to keep the values on both sides of the equals sign equal to one another. This is like a balance. If you add or take away something from one side of the balance it would become unbalanced. But if you do it to the other side, it becomes balanced again.

Student: That makes sense! So adding the 13 to the other side with the number 22, the problem would look like this:

Mentor: Yes, and now we do the simple operations. What is 13 + 22?

Student: 35. So x = 35!

Mentor: Great! Let's check that to be sure. If we replace the "x" in the equation 22 = x - 13 with our answer, 35, we get 22 = 35 - 13. Is that a true statement?

Student: Yes!

Mentor: Let's try another problem that looks a little different:

Mentor: What is different about this problem?

Student: Well, instead of having a number added to the "x", there is a number in front of the "x". I think that means that you should multiply "x" and the 8.

Mentor: Very good. The 8 is the coefficient of the "x".

Student: So we are trying to find a number that when you multiply it by "x" you get 16.

Mentor: Very good. Remember earlier that we needed to get the "x" by itself on one side of the equals sign? Well, we still need to do that, but we won't use addition or subtraction.

Student: Couldn't we use division? Since it is 8 times "x", the opposite of multiplication is division and we could divide.

Mentor: Exactly. We will divide both sides by the coefficient of "x".

Student: 16 divided by 8 is 2, so that is what is on the left side. What is on the right side?

Mentor: Well, we have to divide both sides by 8 for it to remain balanced. What is 8 divided by 8?

Student: One. And then there is the x. So 2 = x. Cool!

Mentor: Let's check our answer:

Mentor: You are right. Now whenever you have a problem with a coefficient of x, you will divide by the coefficient. Let's practice!