Basic Properties of Numbers: Solving Inequalities

[Analysisfreak]

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

 

[epkid08]

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).

 

[HallsofIvy]

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!