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.

- anonymous

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- phi

you can use <= or less than or equal

- anonymous

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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## More answers

- anonymous

Yes that's correct

- anonymous

So like distribute a 12 in?

- phi

yes, but on both sides

- anonymous

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

- phi

yes, now distribute the 3

- anonymous

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

- phi

now combine "like terms"

- phi

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

- anonymous

9x+4 <=16

- phi

now add -4 to both sides

- anonymous

9x <=12?

- phi

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

- anonymous

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)

- anonymous

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

- anonymous

Yes

- anonymous

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

- anonymous

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

- anonymous

How do I post the picture tho?

- phi

click on "attach file"

- anonymous

It doesn't say that for me

- phi

are you at a computer or using the iPad app?

- anonymous

I'm on my phone

- phi

do you see a paper clip icon ?

- anonymous

just got on laptop
gimme a sec

- anonymous

##### 1 Attachment

- phi

do you see what they did wrong?

- anonymous

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

- anonymous

oh. orry

- anonymous

sorry*

- phi

of course that changes everything.

- anonymous

yeah

- phi

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

- anonymous

let me try

- anonymous

im stuck at -x+4<=16

- phi

add -4 to both sides

- anonymous

i subtract 4 and then divide by -1 right?

- anonymous

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

- anonymous

okay :)

- anonymous

thanks so much!

- phi

yw

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