Question

x/4x+1 < 5x/6 solve the inequality answer in interval notation and show work - thanks

Answer 1

I 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

Answer 2

Poswt it.