## anonymous one year ago Someone please help me step by step i've been stuck on this and i want to learn 1. D = p(3 + nr) solve for r

1. Hero

@milli_lovesyouu begin by dividing both sides by p.

2. anonymous

D/p = (3+nr) ?

3. Hero

Very good. Now 3 + nr isn't being multiplied by anything anymore so the parentheses are no longer needed. You can remove them.

4. anonymous

okay so then i have to get rid of the n right?

5. Hero

The next step after removing the parentheses is to subtract 3 from both sides.

6. anonymous

-3d/p = nr ?

7. Hero

The right side is correct, but the left side is incorrect. You wrote -3 as multiplying d/p, but what you actually what to do is subtract 3 from d/p. Have an idea of how to write that?

8. anonymous

no idea :(

9. Hero

How do you write six minus 3?

10. anonymous

6 - 3

11. anonymous

3 - d/p ?

12. Hero

How do you write one-third minus 3?

13. Hero

Very good. How do you write d/p minus three?

14. anonymous

d/p - 3 = nr?

15. Hero

Yes, correct. Subtracting 3 from d/p means the same as d/p minus three. You should pay very close attention to the way math phrases are worded. Now the last step is important and I want you to get it right. First I want you to place everything on the left side in parentheses.

16. anonymous

no idea im sorry i tried on paper but it didnt make sense to me

17. Hero

Type it first in here. I'll explain it later. Just simply place the expression on the left side within a set of parentheses.

18. anonymous

d/p is outside the ( ) right ?

19. Hero

The entire expression on the left side, put parentheses around it.

20. anonymous

(d/p - 3) = nr then, multiple both sides by n?

21. Hero

The expression above is correct as written. Notice that n is being multiplied by r. So to undo that, we have to actually perform an inverse operation. DIVISION. Divide both sides by n.

22. Hero

The final expression is going to look kind of awkward, I know, but no one says the equations have to look pretty.

23. Hero

You're changing it to something else. When you put the expression in parentheses, YOU CANNOT alter it. It's ONE expression. You divide the entire expression by n.

24. anonymous

okay, so it'll be (d/p - 3) / n = r ?

25. Hero

Exactly correct.

26. Hero

And if you're confused about how that looks on paper, it will look like this: $$\dfrac{\dfrac{d}{p} - 3}{n} = r$$

27. anonymous

28. Hero

Yes

29. anonymous

these are my answer choices though ?

30. anonymous

@Hero

31. Hero

It's unfortunate that they have done that, because now they basically want you to re-write it in a different form.

32. anonymous

can you help me? :( please

33. Hero

No wonder you were confused about how to write the final form.

34. anonymous

yea i was looking at my book and other examples but i couldn't figure it out for nothing

35. Hero

It will be more difficult to explain based on the manipulation necessary to re-write it in the proper form.

36. anonymous

its okay ill just email my teacher about it i guess

37. anonymous

Thank you so much for all your help!

38. Hero

Why do you need to email your teacher about it? Have you given up on solving this?

39. anonymous

what other way can i write this?

40. anonymous

i was looking at answer choice a at first

41. Hero

The next step is to first re-write it this way: $$\dfrac{1}{n}\left(\dfrac{d}{p} - 3\right) = r$$ Believe it or not, the expression on the left is equivalent to the expression we got for our initial answer.

42. Hero

Next, you distribute $$\dfrac{1}{n}$$ over $$\dfrac{d}{p} - 3$$ to get $$\dfrac{d}{pn} - \dfrac{3}{n}$$

43. Hero

Afterwards multiply $$\dfrac{3}{n}$$ by $$\dfrac{p}{p}$$ to get $$\dfrac{3p}{p}$$ So the expression on the left now looks like $$\dfrac{d}{pn} - \dfrac{3p}{pn}\ 44. Hero Notice the denominators are the same so we can combine the expression to get: \(\dfrac{d - 3p}{pn} = r$$

45. anonymous

So, A right?

46. Hero

A is correct but the important thing to know is how to get A. You can't get it by eyeballing it and you should never try to guess with problems like these.

47. anonymous

yea, i like explanations so i learn because these problems are on my next test :( im in college intermediate Algebra

48. anonymous

Thank you so much!!!!