[tex]a) \\\\\frac3{x-2} \geq 1\\x-2 > 0 /+2\\x > 2\\D\in (2; \infty)\\\\\frac{3}{x-2} \geq 1 /*(x-2)\\3 \geq x-2 /+2\\5 \geq x\\x \leq 5\\\\x\in(2; 5 >[/tex]
[tex]b) \\\\\frac{2x+7}{x-4} > 3\\\\x-4 > 0 /+4\\x > 4\\D\in (4; \infty)\\\\\frac{2x+7}{x-4} > 3 /*(x-4)\\2x+7 > 3(x-4)\\2x+7 > 3x-12\\7+12 > 3x-2x\\19 > x\\x < 19\\\\x\in(4; 19)[/tex]
[tex]c) \\\\\frac2{4-x} < 3\\\\4-x < 0 /+x\\4 < x\\x > 4\\D\in(4; \infty)\\\\\frac2{4-x} < 3 /*(4-x)\\2 < 3(4-x)\\2 < 12-3x\\2-12 < -3x\\-10 < -3x /:(-3)\\\frac{10}3 > x\\x < \frac{10}3\\\\x\in (-\infty; \frac{10}3)U(4; \infty)[/tex]
[tex]d)\\\\\frac{4x-7}{x-2}\leq5\\x-2 < 0 /+2\\x < 2\\D\in (-\infty; 2)\\\\\frac{4x-7}{x-2}\leq 5 /*(x-2)\\4x-7 \leq 5(x-2)\\4x-7 \leq 5x-10\\-7+10 \leq 5x-4x\\3 \leq x\\x \geq 3\\\\x\in(-\infty; 2)U < 3; \infty)[/tex]
[tex]e) \\\\\frac{1-x}x \leq -4\\\\x > 0\\D\in (0; \infty)\\\\\frac{1-x}x \leq -4 /*x\\1-x \leq -4x\\-x+4x \leq -1\\3x \leq -1 /:3\\x \leq -\frac13\\\\x\in < -\frac13; 0)[/tex]
[tex]f)\\\\\frac{2x-2}{x+1} > 2\\2x-2 > 2(x+1)\\2x-2 > 2x+2\\-2 > 2 - \text{nierownosc sprzeczna}\\\\x+1 < 0 /-1\\x < -1\\\\x\in (-\infty; -1)[/tex]
[tex]g)\\\frac{2x+3}{x+3} < 5\\\\\frac{2x+3}{x+3} < 5 /*(x+3)\\2x+3 < 5(x+3)\\2x+3 < 5x+15\\3-15 < 5x-2x\\-12 < 3x /:3\\-4 < x\\x > -4\\\\x+3 < 0\\x < -3\\D\in(-\infty; -3)\\\\x\in(-\infty; -3)U(-4; \infty)[/tex]
[tex]h) \\\\\frac{-7x+2}{x+\frac12}\leq -6\\\\x+\frac12 < 0 /-\frac12\\x < -\frac12\\D\in (-\infty; -\frac12)\\\\\frac{-7x+2}{x+\frac12}\leq -6 /*(x+\frac12)\\-7x+2\leq -6(x+\frac12)\\-7x+2 \leq -6x-3\\-7x+6x\leq-3-2\\-x\leq-5 /*(-1)\\x\geq 5\\\\x\in(-\infty; -\frac12)U < 5; \infty)[/tex]
