These problems fall in to a few different areas of Algebra

These questions are more for verification purposes..... I did the problems but I want to make sure I have the right processes
1) 1/3 t - 7 > 2 or 4 - t > 6 (SOLVE EACH EQUATION AND WRITE THE ANSWER IN INTERVAL NOTAITON)
to start I added 7 to the first equation and subtracted 4 from the 2nd equation....
1/3 t > 9 OR - t > 2
then I took the first one and multiplied by the recip. and multiplied the 2nd one by -1
(3/1) 1/3 t > 9 (3/1) OR t > -2 (my question on the 2nd problem is do I flip the sign when multiplying by a - # or is that only for division?)
t > 27 U t < -2 or would it be (t > -2)
{- inf. , -2} U {27 , inf.}
I hope this makes sense.....

2) 4/(c-5) + (c+1)/2c (PERFORM OPERATIONS ANS SIMPLIFY)
FIND THE COMMON DENOMENATOR 2c(c - 5)
8c/2c(c-5) + c^2 - 4c -5/2c(c-5) combine like terms....
c^2 + 4c - 5/ 2c(c-5) then factor the top part of the fraction to get.....
(c + 5)(c - 1)/2c(c - 5) and you can't cancel anything so we are done?

3) this is a double fraction so I will type it the best I can.....the directions are to simplify
(2/ (x - 9)) -1 over 1 + (5/ (x - 9))
I FOUND THE LCD TO BE (x - 9) so I ended up with
((2/x - 9) - ((x - 9)/(x - 9)) all over ((x - 9)/(x - 9)) + (5/(x - 9)) COMBINE LIKE TERMS AND I GOT.....
((x - 7)/(x - 9)) over ((x - 4)/(x - 9)) NOW THIS IS WHERE I GET CONFUSED CAN YOU PLEASE ASSIST FROM HERE IF ALL THE PRECEDING INFO IS CORRECT.

4) (3w / 2w - 1) -6 = (4 / 2w - 1)
- (3w / 2w - 1)
so....
(2w - 1) - 6 = -3w + 4/2w - 1 (2w - 1)
MULTIPLY BOTH SIDES BY (2w - 1)
12w + 6 = -3w + 4
+3w +3w
---------------------------
15w + 6 = 4
-6 -6
------------------------
15w = -2
divide by 15 and get w = -2/15 right?

THANK YOU!
Heather

For number 1 yes, you need to flip when ever you multiply or divide by a negative number.

It should be t < -2

Also your intervals are written incorrectly. Use "(" or ")" for exclusive and "[" or "]" for inclusive. You can not include infinity so you need to use:

(-inf,-2) or (27,inf)

Notice I use a parenthesis each time because it is up to but not including -2 or 27.

Number 2: looks good to me.
Number 3: There is a problem when you combine like terms. Distribute the negative all the way through
-(x-9) = -x + 9 so you would end up with -x + 11/ x-9 for the top.

From here you need to multiply by the reciprocal. (-x+11)/(x-9) * (x-9)/(x-4)
I will leave the rest for you.

Number 4: It looks like you tried to move the first fraction over the the other side? But a 2w-1 seemed to linger on the left.

Instead, multiply everything by 2w-1 to get rid of those denominators (Remember to multiply 6 by 2w-1)

so you have: 3w -6(2w-1) = 4

Take it from there.

I hope that was helpful

#3:

\(\displaystyle \frac{\frac{2}{x-9}-1}{1+\frac{5}{x-9}}\)

cross multiply:

\(\displaystyle \frac{\frac{2-(x-9)}{x-9}}{\frac{x-9+5}{x-9}}\)

Now, 'flip' and multiply by the reciprocal:

\(\displaystyle \frac{2-(x-9)}{x-9}\cdot\frac{x-9}{x-9+5}\)

Cancel the x-9:

\(\displaystyle \frac{11-x}{x-4}\)

See?.

Thanks guys! Got it!

Heather