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
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These cannot be in the solution of the inequality.
x = -4 can also not be a solution.
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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.
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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
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Solution: x> 9.403
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Cheers,
Stan H.
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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