Solve the following inequality and write using interval notation

Question

x^2 - 22/ x -4 >_ -7/2
this sign > has the slash underneath
Help me!

Answer 1

suspect you mean

(x^2 -22)/(x-4) >/= -7/2

2x^2 - 44 >/= -7 x + 28

2 x^2 + 7 x - 72 >/= 0
for very large positive x this is true
for very large negative x this is true
where is it not true?
(it is a parabola)
when is that zero?
x = [ -7 +/- sqrt (625)]/4
= [-7 +/-25]/4
x = -8 or x = 4.5
so
x</=-8 or x>/=4.5