## MauriceLong 3 years ago Change the word statement into a equation. Use x as the variable. twice a number is equal to five more than four times a number. Complete the corresponding equation underneath the word statement. Twice a number is equal to five more than four times a number

1. tcarroll010

If x is a variable, what is twice that?

2. MauriceLong

2

3. MauriceLong

Im confuse with Math

4. MauriceLong

Can you break it down for me too better understand you

5. tcarroll010

It's ok to be confused, we'll try to get you out of that confused state. "2" is not exactly right because it does not reflect anything to do with the x. Stated another way: If you have "one football" and you get an additional football, what do you have? The answer has to have the word "football" in it. Same with "x". If you have "one x" and you get another "x", what do you have? The answer HAS to have "x" included in it.

6. MauriceLong

2x

7. tcarroll010

Excellent! Believe it or not, that IS real progress. A lot of people have a stumbling block with that. And further "2x" is understood as 2 times x. And that IS important. So, we'll proceed. I'm going to fast forward, but just a little bit. We have "2x = something" because that's how the problem reads. "Five more than 4 times a number" is "5 + 4x". Dose this make sense so far? Stop me at any time, because it is important to get these concepts down right.

8. MauriceLong

so 2x= 5+4x

9. MauriceLong

it makes since. Im catching on with it .

10. MauriceLong

keep going.

11. tcarroll010

Very very good. Next step is to realize that we have 1 term on the left of the "=" and 2 terms on the right. We can add or subtract equal numbers to BOTH sides at the same time to preserve the equality. And we want to do that because we want to get the x's together on one side .

12. MauriceLong

ok. Im confuse right here lol

13. MauriceLong

2x=5+4x

14. tcarroll010

Usually, by convention, the variables are most often seen on the left side. We want to get the 4x out of the right and over to the left. No problem on the confusion bit, Here is where a lot of people get a little confused, so we'll take it slow at first. 2x is a term, like a "package" because it can be separated by addition or subtraction. "5" is a term. And so is "4x". First, recognize what are "terms".

15. MauriceLong

5+4x=2x is this right way

16. tcarroll010

What you just did is not wrong, but it doesn't do too much just yet. Let's look at the right side to see what is meant by "separated" first. On the right (of 2x = 5 + 4x) we have 5 as a term and 4x as a term. They are separated from each other by either addition or subtraction. Two terms on the right. The "4" and the "x" CANNOT be separated, they are part of the same term.

17. tcarroll010

What you did was show symmetry, but that is not too important at this point. We have to get the 2x term and the 4x term on the same side. So, if we take 2x = 5 + 4x and we SUBTRACT 4x from each side, we get 2x - 4x = 5 + 4x - 4x. That keeps the equality because we did the same addition or subtraction to each side. Now, 2x - 4x = 5 + 4x - 4x is the same as 2x - 4x = 5 + (4x - 4x). Can you see what this equals?

18. tcarroll010

It becomes 2x - 4x = 5 + (0). Or 2x - 4x = 5.

19. tcarroll010

We then use the Distributive Law of Multiplication: 2x - 4x = 5 is the same as (2 - 4)x = 5. Stop and let this sink in. This is a very important operation and is the real key to solving this.

20. MauriceLong

oh ok i get it

21. MauriceLong

addition changes too a subtraction

22. tcarroll010

(2 - 4)x = 5 becomes (-2)x = 5. Yes that is a good point. Addition and subtraction are really, really closely associated. Subtraction is just adding a negative. That also is important and can be better realized with examples. Now, (-2)x = 5 is the same as -2x = 5. We only have to divide both sides now by -2.

23. tcarroll010

(-2x) / (-2) = 5 / (-2). I'm using a lot of parenthese to show the operations. (-2x) / (-2) = 5 / (-2) becomes x(-2) / (-2) = 5 / (-2) = x. So, x = -5/2

24. tcarroll010

There is a lot here, but it's all good. We went through a lot of steps, step-by-step, and eventually, you'll be able to short-cut some of these steps. If you do it a lot, you'll eventually breeze through this stuff. It's overwhelming at first and for a while, so I suggest you go over this whole series of posts at least a couple of times. It will be very worth it in the long run.

25. MauriceLong

ok

26. tcarroll010

Pleas tell me if this is making sense, because I don't want to leave you with confusion, because that won't help you out. I'll go over anything, but I want you to get it because learning is very important.

27. MauriceLong

so the answer for twice a number is -2x and the five more than four times a number is

28. MauriceLong

Im really confuse with this algebra

29. MauriceLong

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30. tcarroll010

If we look at the what the problem is asking and we look at it literally, they are asking only for an equation. They never asked for the solution. I just went the step farther and solved it. If that is further on down in your course, then you can settle for just the equation for now and that is 2x = 5+4x and that is really all they want at this time. The actual solution is x = -5/2. So, in a nutshell, 2x = 5+4x is your answer.

31. MauriceLong

Oh ok. this makes alot of since too me now. I understand what you were saying.

32. tcarroll010

So, stick with it, because I think you are starting to get it. You did make a lot of progress here.

33. MauriceLong

thank you so much for helping me with this math. i surely appreciate it alot.

34. tcarroll010

You're a great guy to work with. The best of everything to you.

35. MauriceLong

So if I ever stumble across a hard math problem, od u mindif I msg you too help me with the problem

36. tcarroll010

Any time, but for now, I have to go. Take care of yourself.

37. tcarroll010

One more thing.

38. tcarroll010

I'm relatively new here, but I think you get notified of when I'm connected when you do a "sign-up" by listing yourself as a "fan". Then you already get notified.