BioHazard9064 one year ago Please help Im stuck on the last one. Solve for x: 2 over 5 (x - 4) = 2x.

1. anonymous

$\frac{2}{5}(x-4) = 2x$

2. anonymous

Step : 1 - Multiply by 5 both the sides first.. Step : 2 - Then divide by 2 both the sides.. Step : 3 - Then, subtract $$x$$ from both the sides. Step : 4 - Then, divide by 4 both the sides. Finally, you will get the value of $$x$$..

3. BioHazard9064

so multiply 2 over 5 by 5

4. BioHazard9064

and 2x?

5. anonymous

yes.. What you got after step 1?

6. BioHazard9064

10 over 5

7. anonymous

Just do it, if you are wrong, I will correct, now try, don't hesitate..

8. anonymous

Can't you cancel 5 with 5 there?

9. BioHazard9064

yes

10. BioHazard9064

oh the 5 cancels that 5 leaving me with 2

11. anonymous

$\frac{2}{5}(x-4) \times 5 = 2x \times 5 \\ \frac{2}{\cancel{5}}(x-4) \times \cancel{5} = 10x \\ 2(x-4) = 10x$

12. anonymous

This is what you get after step 1.. Now what you get after step 2??

13. BioHazard9064

then I divide by 2

14. anonymous

yeah do it..

15. BioHazard9064

(x-4)=5x

16. anonymous

Wow, superb..!! :) Now (x-4) you can write it as : x - 4, without brackets too, no harm...

17. anonymous

$$x - 4 = 5x$$

18. anonymous

Now, subtract $$x$$ from both sides which is our 3rd step. Do it..

19. BioHazard9064

-4=5

20. anonymous

LHS is -4.. that is only good, what about RHS?

21. anonymous

$x - 4 \color{red}{- x} = 5x \color{red}{-x} \\ \cancel{x} - 4 \color{red}{\cancel{-x}} = 5x \color{red}{- x} \\ -4 = 5x \color{red}{- x}$

22. anonymous

Now tell me what is $$5x-x$$ = ??

23. BioHazard9064

5

24. anonymous

How?

25. anonymous

I tell you by one more method.. Okay, take $$x =2$$, now $$5x = 5 \times 2 = 10$$

26. anonymous

Is this good? I have taken the value of x = 2, x is any number there, it is variable, it can take any value, so I took its value as 2 just as an example...

27. anonymous

$$5x$$ means $$5 \times x$$ that is 5 is multiplied with $$x$$..

28. BioHazard9064

sorry my computer froze and reset

29. BioHazard9064

so it pasted my last message

30. anonymous

If I take x = 2, then $$5x$$ becomes $$5 \times x = 5 \times 2 = 10$$, this you got?

31. BioHazard9064

yes

32. anonymous

So, you have : |dw:1437505195878:dw|

33. anonymous

You are getting how I got $$5x-x$$ = 4x ??

34. BioHazard9064

yes

35. anonymous

Or you can do it by distributive property too.. $5x - x$ Take $$x$$ common from both: $5x - x \\ 5x - 1x\\x(5-1) \\ x (4) \\ 4x$

36. anonymous

See, if have $$x-x$$, then you will cancel that, if you have $$2x-2x$$, then also you can cancel, both the terms should be same.. But here one is 5x and other is simply x, so it is quite risky to cancel it and get 0 marks for your answer..

37. anonymous

So are you clear how we got 4x ?

38. BioHazard9064

Yes

39. anonymous

Coming back to our original question: We reached: $-4 = 5x - x \\ -4 = 4x$ This is what we got after step 3. Now do step 4..

40. BioHazard9064

1

41. anonymous

Do it properly, what you got on Left Side?

42. BioHazard9064

-1

43. anonymous

And on right side??

44. BioHazard9064

1

45. anonymous

See, an equation has two sides and = sign in between, so write them fully when you are writing: So after 4th step you get: $-1 = 1x \\ -1 = x \\ .. \\ \color{green}{x = -1}$

46. anonymous

Don't forget the x you are having on right side, why are you not considering x there?

47. BioHazard9064

I did

48. BioHazard9064

49. anonymous

$-4 = 4x \\ \text{Divide by 4 :} \\ \frac{-\cancel4}{\color{red}{\cancel{4}}} = \frac{\cancel{4}x}{\color{red}{\cancel{4}}} \\ -1 = x$

50. anonymous

The value of $$x$$ is $$-1$$..

51. BioHazard9064

Thank you for helping me to understand and not just giving me the answer

52. anonymous

It is okay buddy, we are here to learn and get learned... :)

53. BioHazard9064

true