Question

$\frac{3-x}{3} - \frac{x-2}2} \geq 1$

Answer 1

Como 2 e 3 são primos, MMC(2,3) = 2·3 = 6

6 é o nosso denominador comum.


$2 \cdot \dfrac{3-x}{6}- 3 \cdot \dfrac{x-2}{6}\ge 1 \iff 2(3-x) - 3(x-2) \geq 1 \cdot 6\\\\ \iff 2\left(-x+3\right)-3\left(x-2\right)\ge \:6\\\\ \iff -2x+6-3x+6 \ge \:6\\\\ \iff -5x\ge \:-6\\\\ \iff -\left(-1\right)\cdot \:5x\le \:-\left(-1\right)\cdot \:6\\\\ \iff \dfrac{5x}{5}\le \dfrac{6}{5}\\\\ \iff x\le \dfrac{6}{5}$