Solve the inequality (x/2) > (-8)/(x + 4) + 3 for domain

- anonymous

Solve the inequality (x/2) > (-8)/(x + 4) + 3 for domain

- jamiebookeater

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- amistre64

is the "3" in the denominator??

- anonymous

The 3 is added on after the fraction so I suppose its + 3/1

- amistre64

x -8
-- > ----- + 3
2 x+4
get common denoms...

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## More answers

- amistre64

(x^2 +4x) > -16 + 6x +24
(x^2 +4x) > 6x + 8
x^2 +4x -6x > 8
x^2 -2x >8
x^2 -2x -8 > 0

- amistre64

(x-4)(x+2) >0
when x = -2 or 4; the equation = 0; so lets draw a number line:
<.......-2...........4..........>
- + +
- - +
---------------------
+ - +

- amistre64

this tells us that when:
x = -2, everything to the left is (-) and to the right is (+)
x = 4, everything to the left is (-) and to the right is (+)
We multiply the signs together to get the bottom stuff;
our answer is everything that is (+); becasue that is greater than zero.
(-inf,-2) OR (4,inf)

- anonymous

hmmm that doesnt appear to be one of the answers but ill double check the work

- amistre64

try x= -2
(-2/2) > (-8)/(-2 + 4) + 3
-1 > -8/2 + 3
-1 > -4 + 3
-1> -1... -2 is one of the "options" there :)

- amistre64

try x= 4
(4/2) > (-8)/(4 + 4) + 3
2 > -8/8 + 3
2 > -1 + 3
2> 2... 4 is the other "option" there :)

- amistre64

we know zero is between them, so lets see if we include that or exclude that area...
try x= 0
(0/2) > (-8)/(0 + 4) + 3
0 > -8/4 + 3
0 > -2 + 3
0> -1 is a false statement so the area that has "0" in it is thrown out; that only leaves:
(-inf,-2) U (4,inf)

- anonymous

These are the answers available:
A. (- inf, -4) U (-2, 4)
B. (- inf, -4) U [-2, 4]
C. (-4, -2] U [4, inf)
D. (- inf, -4] U [-2, 4)
E. (-4, -2) U (4, inf)

- amistre64

Check the problem, did you typo a sign?

- anonymous

x -8
--- > ---- + 3
2 x+4

- amistre64

i see an error on my part :) for starters 0 IS > -1, so zero is a solution

- amistre64

never mind that comment, its my senility taking riit :)

- amistre64

root... its like my fingers are having a stroke ....

- amistre64

there is no "equal to" line in the equaiton, so it aint gonna have any [...] in it;

- amistre64

I think it narrows down to "E"
-6/2 = -3
-3 > -8 + 3
-3 > -5 is true, so -6 is a solution so "E" is wrong.
You got something messed up in either the answers or the questions; because the 2 dont match up.... unless you can see an error in my calculations

- amistre64

and -4 is not an option; becasue that zeros out the denom....

- anonymous

I plugged it into my calculator and im trying to eye it from the graph

- amistre64

no -4 and no 0
A. --------------
B. ---------------
C. (-4, -2] U [4, inf)
D. --------------
E. (-4, -2) U (4, inf)

- amistre64

there is no "greater than or EQUAL TO" sign in it so no "[4"
4/2 > -8/8 +3
2> -1 +3
2>2 ...... bad statement
A. --------------
B. ---------------
C. -------------
D. --------------
E. (-4, -2) U (4, inf)
test for "E"?

- amistre64

x = -6
-6/2 = -8(-6+4) + 3
-3> -8/-2 + 3
-3 > 4+3 = 7...... -6 is a bad number and anything on that end...
the answer is "E" then

- anonymous

I plugged it into my calculator and im trying to eye it from the graph

- anonymous

I keep retrying it but it keeps turning out wrong! grrr

- amistre64

use a pencil and paper ;)

- anonymous

I did, ive solved it 4 times now :/

- amistre64

we know that -2 and 4 are boundaries; we know that zero is not an option; we know that {4 is not an option becasue there is no ">=" in the equation; that leaves "E" as the only possible shot.
the only thing we need to determine is if it ends at -4 or not; so plug in a -6 and see if it hold :)

- amistre64

-6 is bad value, so "E" is correct.

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