SOLUTION: Solve: {{{ 2 /(x^2-1) >= -3 }}} Include a sketch to support answer. I isolated x to get{{{sqrt ( 3 )/3}}} and {{{-sqrt( 3 )/3}}} but I don't understand how x is greater th

Question 553110: Solve:

Include a sketch to support answer.
I isolated x to get and but I don't understand how x is greater than or equal to and less than or equal to . I also don't know how to do the sketch.
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Multiply both sides by

Multiply both sides by . Don't forget to reverse the sense of the inequality because of multiplying by a number less than zero.

Add 1 to both sides:

Now when you take the root of bothsides, recognize that

Which is to say that

or

Draw a number line. Put a filled in dot at . Make a fat arrow going to the right with an arrowhead indicating it goes on forever. Put a filled in dot at . Make a fat arrow going to the left with an arrowhead indicating it goes on forever.

John

My calculator said it, I believe it, that settles it

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve:
2 /(x^2-1) >= -3
------
x cannot be -1 ; x cannot be +1
------
Draw a number line and plot x = -1 and x = 1
----
-----
Solve the Equality:
2 = -3(x^2-1)
2 = -3x^2+3
3x^2 = 1
x^2 = 1/3
x = +-sqrt(3/3)
------
Plot those values on the number line.
--------------
You now have values at -1, -1/sqrt(3), 1/sqrt(3), +1
Find the solution set by testing a value in each
of the resulting 5 intervals:
----
2 /(x^2-1) > -3
Test x = -10:: 2/(99)> -3 ; true ; solutions in (-oo,-1)
Test x = -3/4 ; 2/(-7/16) > -3 ; false
Test x = 0 ; 2/-1 > -3 ; true ; solutions in [-sqrt(1/3),sqrt(1/3]
Test x = +3/4 ; 2/(-7/15) > false
Test x = 10 ; 2/99 > -3 ; true ; solutions in (1,+oo)
=========================================================
Cheers,
Stan H.
==========
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