SOLUTION: cant seem to figure this one out :/ {{{x/2

SOLUTION: cant seem to figure this one out :/ {{{x/2 > x/(x+4) + 4 }}}

Question 263516: cant seem to figure this one out :/

Found 2 solutions by stanbon, drk:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x/2 > x/(x+4) + 4
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Solve the equality:
(x/2) = x/(x+4) + 4
Multiply thru by 2(x+4) to get:
x(x+4) = 2x + 8(x+4)
x^2+4x = 2x + 8x + 32
x^2 -6x - 32 = 0
x = [6 +- sqrt(36 -4*-32)]/2
x = [6 +- sqrt(164)]/2
x = 9.403 or x = -3.403
---
These cannot be in the solution of the inequality.
x = -4 can also not be a solution.
--------------------------
Draw a number line and plot -4, -3.403 and 9.403
That breaks the number line into four intervals that
may or may not contain solutions for the INEQUALITY.
------------------------
Test a value from each interval in x/2 > x/(x+4) + 4
Test x = -5: -5/2 > -5/-1 + 4 ; false
Test x = 1: 1/2 > 1/5 + 4 ; false
Test x = 10: 5 > (10/14) + 4 : true
==========================================
Solution: x> 9.403
==========================================
Cheers,
Stan H.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Step 1 - multiply by common denominator of 2(x+4) to get

step 2 - simplify both sides to get

combine like terms to get

set > 0, to get

we have to factor via quadratic to get
x < -3.403 AND x > 9.403
the values in these ranges will give us positive answers.
However, we have a restriction at x = -4. So in interval notation
(-00, -4) u (-4, -3.403) u (9.403, +00)
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