Question

Решите неравенство
х+2х-1 - 13х-1 больше или равно х-2
___ ___ ___
5 15. 3

Answer 1

$x+\frac{2x-1}{5}-\frac{13x-1}{15}\geq \frac{x-2}{3}\; \Big|\cdot 15\\\\15x+3(2x-1)-(13x-1)\geq 5(x-2)\\\\15x+6x-3-13x+1\geq 5x-10\\\\8x-2\geq 5x-10\\\\3x\geq -8\\\\x\geq -\frac{8}{3}\\\\x\geq -2\frac{2}{3}$

Answer 2

$x \geq \frac{-8}{3}$

Объяснение:

$x + \frac{2x-1}{5} -\frac{13x-1}{15} \geq \frac{x-2}{3}$

$\frac{15x + 3(2x-1) - (13x-1) - 5(x-2)}{15} \geq 0$

$\frac{15x + 6x - 3 - 13x + 1 - 5x + 10}{15}\geq 0$

$\frac{3x+8}{15} \geq 0$

$3x + 8 \geq 0\\\\3x \geq -8\\\\x \geq \frac{-8}{3}$