Question

Is this correct?

solve the rational inequality in interval notation
(x+9)(x-11)/x+7 ≤ 0

My answer is (-9,-7)∪(-7,11)

Answer 1

um
first note that x=-7 is not allowed in the soltions set
multiply both sides by x+7
make a sign chart and input values and see what they are

ok so we know we have zeroes at x=-9 and x=11
and x=-7 is not allowed so

see attachment


at x=-10,, we get a negative sign so it is less than 0
at x=-8, we get a positive sing, so it is more than 0
at x=-3, we get a negative sign, so less than 0
at x=20, we get a positive sign,so greater

so then

we do from negative inity to -9
and not between -9 and -7
between -7 and 11
so then

(-infinity,-9)U(-7,11]