Question

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.

Answer 1

you can use <= or less than or equal

Answer 2

Okay

Answer 3

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 ?

Answer 4

Yes that's correct

Answer 5

So like distribute a 12 in?

Answer 6

yes, but on both sides

Answer 7

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

Answer 8

yes, now distribute the 3

Answer 9

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

Answer 10

now combine "like terms"

Answer 11

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

Answer 12

9x+4 <=16

Answer 13

now add -4 to both sides

Answer 14

9x <=12?

Answer 15

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

Answer 16

Ok

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

Are you sure we started with the correct problem?

for the problem I posted we get
x <= 4/3

Answer 21

Yes

Answer 22

I'm confused hsha

Answer 23

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)

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

take a screen shot or a picture

Answer 28

How do I post the picture tho?

Answer 29

click on "attach file"

Answer 30

It doesn't say that for me

Answer 31

are you at a computer or using the iPad app?

Answer 32

I'm on my phone

Answer 33

do you see a paper clip icon ?

Answer 34

just got on laptop
gimme a sec

Answer 35

do you see what they did wrong?

Answer 36

they didnt change the 4/3?

Answer 37

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

Answer 38

oh. orry

Answer 39

sorry*

Answer 40

of course that changes everything.

Answer 41

yeah

Answer 42

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

Answer 43

let me try

Answer 44

im stuck at -x+4<=16

Answer 45

add -4 to both sides

Answer 46

i subtract 4 and then divide by -1 right?

Answer 47

then the sign flips

Answer 48

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

Answer 49

okay :)

Answer 50

thanks so much!

Answer 51

yw