Basic Properties of Numbers: Solving Inequalities

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The discussion focuses on solving the inequality 5 - x² < 8. The solution process involves rearranging the inequality to -x² < 3, leading to x² > -3. It is established that since x² is always non-negative, the inequality holds true for all real numbers. Therefore, the solution set for x is (-∞, ∞).

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Homework Statement


Find all number x for which 5-x^2 < 8


Homework Equations





The Attempt at a Solution


Adding -5 from both sides we get -x^2 < 3
x^2 > -3
then it is impossible that x > sqrt -3...
Any idea how to solve this step bystep
 
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If you think about, you're asking when is five minus a positive number less than eight, and the answer to that is always, (-\infty, \infty).
 
Analysisfreak said:

Homework Statement


Find all number x for which 5-x^2 < 8


Homework Equations





The Attempt at a Solution


Adding -5 from both sides we get -x^2 < 3
x^2 > -3
then it is impossible that x > sqrt -3...
Any idea how to solve this step bystep

Not only is it possible for x2 to be greater than -3, since x2 is always non-negative it is always true!
 

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