Question

For x+3/x-4 is less than or equal to 0, why is the interval notation [3,4)?

Answer 1

x+3/x-4 <= 0
now you have to be careful when multiplying by x-4.

if x-4 > 0, then x+3 <= 0 so x <= -3
But x>4, so it cannot be <= -3

if x-4 < 0 then x+3 >= 0 x >= -3
But x<4, so -3 <= x < 4 ... x in [-3,4)