Math
posted by Alex on .
I need help on how to solve this type of problem please.
29.)Solve the inequality and express the solution in terms of intervals whenever possible.
1/(x2) ≥ 3/(x+1)
THE ANSWER IS: ( ∞,1 ) U ( 2,(7/2) ]

1/(x2)  3/(x+1) ≥ 0
So we have critical values at x = 1 and x = 2
test for any value x < 1, e.g. x = 10
is 1/12 ≥ 3/9 ? YES
test for any value between 1 and 2, say x = 1
is 1/1 ≥ 3/2 ? NO
test for any value x > 2, say x = 5
is 1/3 > 3/6 ? YES
so solution is
x < 1 OR x > 7/2
suggestion:
enter 1/(x2)  3/(x+1)
into "first graph" of
http://rechneronline.de/functiongraphs/
to see where the graph is above the xaxis.