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## anonymous one year ago s=1/2n(a+K) could someone show me how to do this? im confused because i thought you had to multiply the entire equation by 2 but thats giving me wrong answer

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1. freckles

There isn't enough information in this question.

2. anonymous

solving for K

3. freckles

$s=\frac{1}{2}n(a+K) ?$ If this is right, yes multiplying 2 as a first step is good. But that still will not isolate K yet. You will still have to perform more steps. Is this what you get when you multiply 2 on both sides? 2s=n(a+K) try isolating (a+k) next by undoing the multiplication by n to it.

4. anonymous

Yeah I get that part I'm just wondering why I dont multiply a and K by 2 and it ends up being 2s=n(a+K) instead

5. freckles

are you asking why 2/2=1?

6. anonymous

|dw:1443585029131:dw|

7. freckles

but 2/2=1

8. freckles

why you multiply one side by 4 and the other side by 2?

9. freckles

|dw:1443585130255:dw|

10. freckles

|dw:1443585146509:dw|

11. anonymous

oh i see

12. anonymous

i dont know i was just under the impression that if you multiply by 2 you have to do that to the entire problem but it ends up being 1 so its just a+K

13. freckles

well you have n(a+k) on the right hand side but yes you multiply 2 on both sides

14. freckles

whereas you were multiplying 2 on one side and 4 on the other side

15. anonymous

i was canceling out the 1/2n and just putting it as n but also multiplying 2*a and 2*k because i thought when clearing fractions you had to multiply the entire equation and not just one part of it i wasnt using 4

16. freckles

you were though you multiply by 2 and then you multiply by another 2 on the right hand side and 2*2 is 4

17. freckles

see this is what you get on the right hand side side if you multiply by 4 $4 \cdot \frac{1}{2} n (a+K) \\ \frac{4}{2}n(a+k) \\ 2n(a+k) \\ n(2a+2k)$ which is what you receive in the end on your right hand side

18. anonymous

|dw:1443585661985:dw|

19. anonymous

i was doing it like that

20. freckles

what happen to your n in the end? and you are still multiplying 2 on left hand side and 4 on the right hand side this incorrect you multiply both sides by the same number $s=\frac{1}{2}n(a+k) \\ 2 \cdot (s)=2 \cdot (\frac{1}{2}n(a+k)) \\ 2s=(2 \cdot \frac{1}{2})n(a+k) \text{ since multiplication is associative } \\ 2s=(1)n(a+k) \text{ since } \frac{2}{2}=1 \\ 2s=n(a+k) \\ \text{ now try dividing both sides by } n \\ \frac{2s}{n}=a+k$ there is one last step to perform

21. anonymous

oh it makes sense

22. anonymous

i was distributing it wrong when its already being canceled out

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