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This is a multiple choice question, with possible answers:
(a) -3 < x < 3;
(b) 0 < x < 4;
(c) 1 < x < 3;
(d) -1 < x < 9;
(e) -3 < x < -1.
Let's start by rearranging the inequality to get
x^4 - 8x^2 - 9 < 0.
Now, we notice that x^4 = (x^2)^2, and so what we have on the left-hand side of our inequality above is really a quadratic equation in x^2:
(x^2)^2 - 8x^2 - 9 < 0.
So we can factor this like a normal quadratic: look for two numbers that add to make -8 and multiply to make -9. It turns out that -9 and +1 work, then our inequality is simply
(x^2 - 9)(x^2 + 1) < 0.
If we multiply two numbers together, the only way for the product to be negative (less than zero) is for one of the numbers to be negative and the other positive. But x^2 is positive no matter what value x takes, and so (x^2 + 1) is definitely going to be positive, for all values of x.
So we have to have (x^2 - 9) negative:
x^2 - 9 < 0.
x^2 < 9,
-3 < x < 3,
i.e. the answer is (a).see more