Question

18 Rezolvaţi inecuațiile:​

Answer 1

Răspuns:

$a ) \frac{x+1}{3}-\frac{1}{2}\geq \frac{x}{6} \\\\2(x+1)-3\geq x\\2x+2-3\geq x\\2x-1\geq x\\2x-x\geq 1\\x\geq 1$

$b)x\sqrt{2} -1 < x\sqrt{8}+|-1| \\\sqrt{2} x -1 < x*2\sqrt{2}+1\\\sqrt{2}x-1 < 2\sqrt{2}x+1\\\\ \sqrt{2}x -2\sqrt{2} x < 1+1\\-\sqrt{2} x < 2\\x > -\frac{2}{\sqrt{2} } \\x > -\sqrt{2}$

$c) \frac{2*x}{-3}+\frac{1}{-4} < \frac{x}{-6} +\frac{5}{-12} \\-\frac{2x}{3} -\frac{1}{4} < \frac{x}{6} -\frac{5}{12} \\-8x-3 < 2x-5\\-8x-2x < -5+3\\-10x < -2\\x > \frac{1}{5}$

$d) 3(x-\frac{1}{3}) -2(x+\frac{1}{2})\leq 4(x-\frac{1}{4} )\\3x-1-2x-1\leq 4x-1\\3x-2x-1\leq 4x\\x-1\leq 4x\\x-4x\leq 1\\-3x\leq 1\\x\geq -\frac{1}{3}$

Mult succes!