Question

The solution set of $x-2>0,x-9<0$ and $x^2-9\ge 0$ is

• A. $[3,9]$
• B. $[3,9)$
• C. $(3,9]$
• D. $(3,9)$

Answer 1

The correct option is B $[3,9)$

$x-2>0\Rightarrow x>2\cdots \left(1\right)x-9<0\Rightarrow x<9\cdots \left(2\right)x^2-9\ge 0\Rightarrow (x+3)(x-3)\ge 0\Rightarrow x\in (-\infty ,-3]\cup [3,\infty )\cdots \left(3\right)$
From $\left(1\right),\left(2\right)$ and $\left(3\right)$,
$x\in [3,9)$