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.

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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.

Mathematics
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  • phi
you can use <= or less than or equal
Okay
  • 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 ?

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Other answers:

Yes that's correct
So like distribute a 12 in?
  • phi
yes, but on both sides
12x-5+3 (3-x) <= 16?
  • phi
yes, now distribute the 3
12x-5+9-3x <=16
  • phi
now combine "like terms"
  • phi
12 x's take away 3 x's and -5+9
9x+4 <=16
  • phi
now add -4 to both sides
9x <=12?
  • phi
yes. now divide both sides by 9 (remember it's ok to divide by positive numbers)
Ok
  • phi
\[ \frac{9x}{9} \le \frac{12}{9} \] and 9/9 on the left side simplifies to 1
  • phi
and we can simplify 12/9 (divide top and bottom by 3)
Uhm but I think the answer is supposed to be x greater than or equal to -12
  • phi
Are you sure we started with the correct problem? for the problem I posted we get x <= 4/3
Yes
I'm confused hsha
  • 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)
  • phi
Here are the possible problems: 1) typo in the problem 2) typo in answer key
Wait... it's actually a problem that some one did and I have to explain where they went wrong
  • phi
maybe if you post a copy of the page...
  • phi
take a screen shot or a picture
How do I post the picture tho?
  • phi
click on "attach file"
It doesn't say that for me
  • phi
are you at a computer or using the iPad app?
I'm on my phone
  • phi
do you see a paper clip icon ?
just got on laptop gimme a sec
1 Attachment
  • phi
do you see what they did wrong?
they didnt change the 4/3?
  • phi
yes. as for *our problem* we started with (12x-5)/12 and it should be (2x-5)/12
oh. orry
sorry*
  • phi
of course that changes everything.
yeah
  • phi
can you do the work ? this one is more tricky because we will get a negative x
let me try
im stuck at -x+4<=16
  • phi
add -4 to both sides
i subtract 4 and then divide by -1 right?
then the sign flips
  • 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
okay :)
thanks so much!
  • phi
yw

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