Question

Am nevoie de ajutor la Ex 10 .Dau cel mai bun răspuns .Va rog !

Answer 1

$\it |3x+1| < 7 \Rightarrow -7 < 3x+1 < 7\Big|_{-1} \Rightarrow -8 < 3x < 6\Big|_{:3} \Rightarrow -\dfrac{8}{3} < x < 2 \Rightarrow \\ \\ \\ \Rightarrow A=\Big(-\dfrac{8}{3},\ 2\Big)\\ \\ \\ |2x-1|\leq5 \Rightarrow -5\leq2x-1\leq6\Big|_{+1} \Rightarrow -4\leq2x\leq7\Big|_{:2} \Rightarrow -2\leqx\leq\ 3,5 \Rightarrow \\ \\ \\ \Rightarrow B=[-2;\ \ 3,5]$

$\it \Big|\dfrac{x+5}{2}\Big|\leq1 \Rightarrow -1\leq\dfrac{x+5}{2}\leq1\Big|_{\cdot2} \Rightarrow -2\leq x+5\leq2\Big|_{-5} \Rightarrow -7\leq x\leq -3 \Rightarrow \\ \\ \\ \Rightarrow C=[-7,\ \ -3]$

$\it -1\leq\dfrac{3x+4}{2}\leq7\Big|_{\cdot2} \Rightarrow -2\leq3x+4\leq14\Big|_{-4} \Rightarrow -6\leq3x\leq10\Big|_{:3} \Rightarrow \\ \\ \\ \Rightarrow -2\leq x\leq\dfrac{10}{3} \Rightarrow F=\Big[-2,\ \dfrac{10}{3}\Big]$