Giải thích các bước giải:
1)đkxđ $x\ge -\dfrac 32$
$\sqrt{2x+3}+\sqrt{x+2}\le 1$
$\to\sqrt{2x+3}\le 1-\sqrt{x+2}$
$\to 2x+3\le (1-\sqrt{x+2})^2$
$\to 2x+3\le 1+x+2-2\sqrt{x+2}$
$\to x\le -2\sqrt{x+2}$
$\to x^2\le 4(x+2)$
$\to -2\le x\le -2\sqrt{3}+2$
$\to -\dfrac 32 \le x\le -2\sqrt{3}+2$
2)Đkxđ $1\le x\le 11$
$\sqrt{11-x}-\sqrt{x-1}>2$
$\to \sqrt{11-x}>2+\sqrt{x-1}$
$\to 11-x>(2+\sqrt{x-1})^2$
$\to 11-x>4+4\sqrt{x-1}+x-1$
$\to 8-2x>4\sqrt{x-1}$
$\to 4-x>2\sqrt{x-1}$
$\to x-1+2\sqrt{x-1}-3<0$
$\to (\sqrt{x-1}+3)(\sqrt{x-1}-1)<0$
$\to \sqrt{x-1}<1$
$\to x<2$
$\to 1\le x<2$
