How do solve $1/x^2-1<=0$ graphically?

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Answer 1 · 2018-01-09T23:16:43

$x<=-1 or x>=1$

$1/x^2 - 1 <= 0$

First, add 1 to both sides so that you end up with $1/x^2$ on the left, to make graphing a bit easier

$1/x^2 <= 1$

Then, plot the graph of $y=1/x^2$

graph{1/x^2 [-10, 10, -5, 5]}

To find the range of x for which $1/x^2 <= 1$ is true, just find the range of x for which $y<=1$ in the graph above

graph{(y-1/x^2)(y-1)=0 [-10, 10, -5, 5]}

As you can see from this graph, $1/x^2$ drops below $y=1$ when $x<=-1$ and $x>=1$

Thus the solution to $1/x^2 <= 1$ , and thus $1/x^2 -1 =0$ , is $x<=-1 or x>=1$

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