Question

x=? [x]=3
[2x]=2
[3x+1 supra 2]= 5
va roogg repede​

Answer 1

Răspuns:

[3;4)

[1;1,5)

[3;11/3)

Explicație pas cu pas:

*

x∈[3;4)

**

2x∈[2;3)

x∈[1;1,5)

***

5≤(3x+1)/2<6

10≤3x+1<12

9≤3x<11

x∈[3,11/3)

Answer 2

$\it [x]=3 \Rightarrow x\in [3,\ \ 4)\\ \\ \ [\it2x]=2 \Rightarrow 2x\in[2,\ 3)|_{:2} \Rightarrow x\in[1;\ 1,5)$

$\it\Big[ \dfrac{3x+1}{2}\Big] =5 \Rightarrow 5\leq\dfrac{3x+1}{2}<6|_{\cdot2} \Rightarrow 10\leq3x+1<12|_{-1} \Rightarrow \\ \\ \\ \Rightarrow 9\leq3x<11|_{:3} \Rightarrow3\leq x<\dfrac{11}{3} \Rightarrow x\in\Big[3,\ \dfrac{11}{3}\Big)$