Zadanie Rozwiąż nierówności: a) |15-3x| ≤ 5 b) |3 2/5+x| < 2 1/5 c) |3 2/3 - 1/3x| ≥ 1 d) |x+2 1/2| > 1 1/2
źródło:
a) |15-3x|\leq5 15-3x\leq5 lub -(15-3x)\leq5 -3x\leq-10|/-3 x\geq\frac{10}{3} lub -15+3x\leq5 3x\leq20 x\leq\frac{20}{3} x\in\langle\frac{10}{3}:\frac{20}{3}\rangle
b) |3\frac{2}{5}+x|<2\frac{1}{5} \frac{17}{5}+x < \frac{11}{5}. ........... lub............... -(\frac{17}{5}+x )< \frac{11}{5}. x<\frac{11}{5} - \frac{17}{5} x< -\frac{6}{5} lub - \frac{17}{5} -x < \frac{11}{5}. -x<\frac{11}{5}+\frac{17}{5} |*-1 x> -\frac{28}{5} x\in (-5\frac{3}{5};-1\frac{1}{5})
c) |3 \frac{2}{3} - \frac{2}{3}x| \geq 1 \frac{11}{3} - \frac{2}{3}x \geq \frac{3}{3}.....lub -( \frac{11}{3} - \frac{2}{3}x) \geq \frac{3}{3} - \frac{2}{3}x \geq \frac{3}{3} - \frac{11}{3} - \frac{2}{3}x \geq -\frac{8}{3} |Mnożymy przez (-\frac{3}{2}) x \leq -\frac{8}{3}*(-\frac{3}{2}) x \leq 4| lub - \frac{11}{3} + \frac{2}{3}x) \geq \frac{3}{3} \frac{2}{3}x \geq \frac{3}{3} + \frac{11}{3} x\geq \frac{14}{3}*\frac{3}{2} x\geq 7 x\in(-\infty;4\rangle \cup \langle 7;+\infty)
d) |x+2 \frac{1}{2} |>1 \frac{1}{2}
x+2 \frac{1}{2} >1 \frac{1}{2} lub -(x+2 \frac{1}{2}) >1 \frac{1}{2}
x>\frac{3}{2} - \frac{5}{2}
x>-1 | lub
-x- \frac{5}{2} > \frac{3}{2}
-x> \frac{3}{2} + \frac{5}{2} |*(-1) x< -4 x\in(-\infty;-4)\cup(-1;+\infty)