Question

What is the solution of the inequality 9 - x^2<0?

Answer 1

`x < -3\quad \mathrm{or}\quad \:x > 3`

Explanation:

Given:

`9-x^2 < \:0`

Solve:

`\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}`

`9-x^2-9 < 0-9`

`\mathrm{Simplify}`

`-x^2 < -9`

`Multiply\:both\:sides\:by\:-1\:`

`\left(-x^2\right)\left(-1\right) > \left(-9\right)\left(-1\right)`

`\mathrm{Simplify}`

`x^2 > 9`

`\mathrm{For\:}u^n\: > \:a\mathrm{,\:if\:}n\:\mathrm{is\:even}\mathrm{\:then\:}u\: < \:-\sqrt[n]{a}\:or\:u\: > \:\sqrt[n]{a}`

`x < -√(9)\quad \mathrm{or}\quad \:x > √(9)`

`√(9)=3`

`x < -3\quad \mathrm{or}\quad \:x > 3`

~lenvy~