Question

Sa se determine multimea valorilor reale ale lui x pentru care |5x-3|<2 !

Answer 1

$|5x - 3| < 2$

$1)5x - 3 < 2$

$5x < 2 + 3$

$5x < 5 \: | \div 5$

$x < 1$

$x \: \in \: ( - \infty ,1)$

$2) - 5x + 3 < 2$

$- 5x < 2 - 3$

$- 5x < - 1 \: | \times ( - 1)$

$5x > 1$

$x > \frac{1}{5}$

$x \: \in \: ( \frac{1}{5} , + \infty )$

$S=\left \{ (-\infty ,1)\cap( \frac{1}{5},+\infty)\right \}$