## anonymous one year ago I need help! 12x-5/12 + 3-x/4 < 4/3 *** supposed to be a less than or equal to, but I don't have that sign.

1. phi

you can use <= or less than or equal

2. anonymous

Okay

3. phi

is it $\frac{12x-5}{12} + \frac{3-x}{4} \le \frac{4}{3}$ ? I would multiply both sides by 12 (that means *every* term on both sides) as a first step. can you do that ?

4. anonymous

Yes that's correct

5. anonymous

So like distribute a 12 in?

6. phi

yes, but on both sides

7. anonymous

12x-5+3 (3-x) <= 16?

8. phi

yes, now distribute the 3

9. anonymous

12x-5+9-3x <=16

10. phi

now combine "like terms"

11. phi

12 x's take away 3 x's and -5+9

12. anonymous

9x+4 <=16

13. phi

now add -4 to both sides

14. anonymous

9x <=12?

15. phi

yes. now divide both sides by 9 (remember it's ok to divide by positive numbers)

16. anonymous

Ok

17. phi

$\frac{9x}{9} \le \frac{12}{9}$ and 9/9 on the left side simplifies to 1

18. phi

and we can simplify 12/9 (divide top and bottom by 3)

19. anonymous

Uhm but I think the answer is supposed to be x greater than or equal to -12

20. phi

Are you sure we started with the correct problem? for the problem I posted we get x <= 4/3

21. anonymous

Yes

22. anonymous

I'm confused hsha

23. phi

if the answer is really x>= -12 then x= 2 should work (but won't because we know x<= 4/3 (1 and 1/3) ) using x=2 in the problem $\frac{12x-5}{12} + \frac{3-x}{4} \le \frac{4}{3} \\ \frac{24-5}{12} + \frac{3-2}{4} \le \frac{4}{3} \\ \frac{19}{12} +\frac{3}{12} \le \frac{4}{3} \\ \frac{22}{12} \le \frac{4}{3} \\ 1.833... \le 1.333...$ which is not true (as we know)

24. phi

Here are the possible problems: 1) typo in the problem 2) typo in answer key

25. anonymous

Wait... it's actually a problem that some one did and I have to explain where they went wrong

26. phi

maybe if you post a copy of the page...

27. phi

take a screen shot or a picture

28. anonymous

How do I post the picture tho?

29. phi

click on "attach file"

30. anonymous

It doesn't say that for me

31. phi

are you at a computer or using the iPad app?

32. anonymous

I'm on my phone

33. phi

do you see a paper clip icon ?

34. anonymous

just got on laptop gimme a sec

35. anonymous

36. phi

do you see what they did wrong?

37. anonymous

they didnt change the 4/3?

38. phi

yes. as for *our problem* we started with (12x-5)/12 and it should be (2x-5)/12

39. anonymous

oh. orry

40. anonymous

sorry*

41. phi

of course that changes everything.

42. anonymous

yeah

43. phi

can you do the work ? this one is more tricky because we will get a negative x

44. anonymous

let me try

45. anonymous

im stuck at -x+4<=16

46. phi

47. anonymous

i subtract 4 and then divide by -1 right?

48. anonymous

then the sign flips

49. phi

with relations, if you divide by a negative number you have to remember to flip the relation once you get to -x <= 12 you can divide by -1 and flip to get x >= -12 or , remember it's always safe to add or subtract. so we could add +x to both sides: -x + x <= 12 + x 0 <= 12 + x now add -12 to both sides -12 <= x which can also be written x>= -12

50. anonymous

okay :)

51. anonymous

thanks so much!

52. phi

yw