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September 29, 2016
Posted by **Sara** on Sunday, January 15, 2012 at 1:27pm.

- precalculus -
**Reiny**, Sunday, January 15, 2012 at 4:59pmI will assume you meant

x/(4x+1) < 5x/6

times 6(4x+1)

6x < 20x^2 + 5x

20x^2 - x > 0

x(20x - 1) > 0

critical values: x = 0, x = 1/20 and of course x ≠ -1/4

try values in the intervals

1. x < -1/4, say x = -1

is -1/-3 < -5/6 ? , is 1/3 < -5/6 ? NO

2. between -1/4 and 0, say x = -.2

is -.2/.2 < -1/6 ? , is -1 < - 1/6 ? YES

3. between 0 and 1/20, say x = .01

is .01/1.04 < .05/6 ? , is .0096.. < .00833 ? , NO

4. greater than 1/20, say x = 1

is 1/5 < 5/6 ? Yes

So -1/4 < x < 0 OR x > 1/20

check my arithmetic - precalculus -
**Henry**, Sunday, January 15, 2012 at 5:18pmPoswt it.