(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am doing the HW in Spivak's calculus (problem 4 (ii) ) on inequalities. The problem statement is:

find all x for which

5-x^{2}> 8

3. The attempt at a solution

I know this is a simple problem, but bear with me for a moment. I want someone who is familiar with Spivak to tell me what the right way to do this is. Pretend for a moment that I know virtually nothing (it shouldn't be too hard ) and that all that I know comes from the first chapter in Spivak's textbook. I start the solution like this

5-x^{2}<8

5-x^{2}+ x^{2}-8 < 8 + x^{2}- 8

x^{2}> -3

Now, I am not sure how to 'rigorously' finish the solution. It is clear that this is true for all numbers x. Is it enough to say that

x^{2}= x*x and since we already showed in a previous example that ab > 0 if a,b > 0 OR a,b < 0.

Is that the RIGHT way to do this? Thanks. I am still trying to get a feel for this text and to answer the problems without using any of my prior knowledge.

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# Spivak: Inequality

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