Variables, Expressions and Equations: What's the Difference?

0:00 Variables, expressions, and equations. Let's get started. A closed box of blocks. How many are inside? Add three loose blocks. 1 2 three of them. So, we have this closed box and we're adding three more. Let's call the box X right here. And when we're adding three more, we're going to have a plus three. We're adding three more. And remember, X is a variable, so it's an unknown amount. We're not sure how many are in that box, but we do know we're going to add three more to however many is in that box. How many in all? Well, we can't tell yet. We have no understanding of what is inside the

0:47 box that's labeled X. But now let's add a clue. You can see here we have a scale and on a scale, the center of that scale is our equal sign right here. And we have a left side of the scale and a right side of the scale. The important thing to know is that the left side and the right side, in order for that equal sign for it to be true, they have to equal each other. They have to be the same value on both sides. Let's think about it. Which one can we solve? Can we solve A section right here? An unknown amount X plus three more or could we solve this B section right here?

1:32 Which says an unknown amount plus three more blocks is equal to how many blocks do we have here? We have 1 2 3 4 5 6 7 total blocks. Which one of those can be solved? Only B because it has an equal sign, right? So, we'll we'll we can tell how many are going to be in that box because this scale is balanced. Now remember, an expression is a phrase and an equation is a sentence. In that last one, the expression was the X + 3. And in the last one, the equation was X + 3 = 7. Do you see the difference?

2:18 Remember, a variable is a letter for a number. So, we use letters in algebra to tell us that there is an unknown amount. X stands for a number that we don't know yet. We don't know what's inside the box right now. Any letter will work and we will typically use a lowercase letter. So, in this example, we have lowercase like X, N, A, and Y. An expression is a math phrase. So, we have numbers, letters, signs, but no equal sign on an expression. The equal sign is saved for the equation. So, in these examples, X + 3 is an expression cuz we have X and then we are adding three more.

3:03 2N is an expression. We just have two N's, two unknown amounts. And then 5 + 4, that's an expression. We have five blocks plus four more blocks. An equation is a math sentence. Two sides joined by an equal sign. Again, we still have our X + 3 is equal to 7. That is an equation. The equal sign means both sides are worth the same. X + 3 has to be equal to 7. So, in an expression, we will evaluate or simplify. You won't always get like a final answer unless they give you more information. An equation is when we're going to solve it. All right, let's sort these. Phrase or sentence?

3:50 We're kind of thinking, is this an expression or an equation? All right, let's start off. 5x - 2 That is an expression. There's no equal sign. x + 4 = 9. That's an equation. There's an equal sign. 12 = 3n Still an equation. There's an equal sign. 8 + 6 There's no letter, but it's still an expression cuz there's no equal sign. All right, let's evaluate and we'll open the box. So, in this example x + 3 when x = 4. So, they're telling you now how much is in the box. So, they're saying in that box there's going to be four.

4:37 And we have 4 + 3 now. 4 + 3 That gets us seven. See? Four blocks plus three more blocks. That gets us seven blocks in all. Example three 2n + 1 when n = 5. They're saying we have two n's. So, we have two times n right here. 2 × n + one more. Each box holds five. So, we would have five plus five plus one more, which gets us 10 plus one, which is 11. Simplify. We're going to group what matches. So, in this one we have an x + 2 + x + 3.

5:22 We can put the x's together. And we can put the two and the three together. Because they match. So, boxes with boxes and blocks with blocks. x + x is just 2x. And 2 + 3 gets us five. Which gets us in all just 2x + 5. 2x + 5 Okay, watch out for this mistake that happens a lot. Solve 2x + 5 and instead they write 2x = 5, so x = 2.5. That is definitely not correct. So, be careful with that. 2x + 5 is not the same as 2x = 5. If you have 2x + 5, you can't do anything at this point. It that is simplified. That's an

6:07 expression. You need to have more information. You need to know what x is in order to do more. All right, let's solve with a balance scale. In this equation, we have x + 3 = 7. Going back to the beginning here. You want to take three off both sides. So, you see how we're subtracting these three from this side and this side. So, we had x + 3 = 7. Take away three from both sides. Take away three and you're going to be left with x = 4. And look, here it is. 1 2 3 and 4. x is equal to 4. We can check. You can do it in reverse. 4 + 3 = 7. Remember, an expression

6:53 there's no equal sign and we're going to simplify or evaluate. In an equation, that will have an equal sign and we're just going to solve it. Okay, now it's going to be your turn. So, I'm going to give you the mild problem, the medium problem and the spicy problem. I'll give you the answers to the mild and the medium right now. The spicy problem answer is going to be in the comments. Make sure you take a moment, leave me a comment, let me know what you got for an answer. Mild. Evaluate 9 + a when a is equal to 6. So, remember they're telling you what a is. So, you just want to take this 6 and replace it where you see the a. Medium. x + 5 + x + x. Think about it. Do you have enough information in this

7:38 expression to get an answer or are you just simplifying? Here's the spicy one. 4x + 2 or 4x + 2 = 18. Which one can you solve and what would you get for an answer? All right, for mild the answer was 15 and for medium 3x + 5 cuz you could only simplify that one. Remember, the spicy answer is going to be pinned in the comments, so take a look. If you found value in this video, please take a moment to like and subscribe to the channel and I will see you in the next lesson. Thank you so much. Take care. Bye.