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Slavitescudoraid

</ inseamna mai mic sau egal iar simplu / e supra

ex 1

-5 </ 2x-3 < 7 /+3

-2 </ 2x < 10 /:2

-1 </ x < 5 , M = {-1,0,1,2,3,4}

-5 </ x <3 , N = {-5, -4, -3, -2, -1, 0,1,2}

MUN = {-5, -4, -3, -2, -1, 0,1,2,3,4}

M ∩ N={-1, 0,1,2}

M/N {3,4}

N/M = {-5, -4, -3, -2}

Ex 2

-3 </ 2x-7 </ 3 /+7

4 </ 2x </ 10 /:2

2 </ x </ 5 , A = {2,3,4,5}

-1 </ 2x+1/9 </ 1  /*9

-9 </ 2x+1 </ 9 /-1

-10 </ 2x </ 8 /:2

-5 </ x </ 4, B = {-5,-4, -3, -2, -1, 0,1,2,3,4}

AUB = {-5,-4, -3, -2, -1, 0,1,2,3,4,5}

A∩ B ={2,3,4}

A/B = {5}

B/A={-5, -4,-3,-2,-1,0,1}

Targoviste44id

1.

[tex]\it -5\leq2x-3<7|_{+3} \Rightarrow -2\leq2x<10|_{:2} \Rightarrow -1\leq x<5 \Rightarrow M=[-1,\ 5)\\ \\ -5\leq x<3 \Rightarrow N=[-5,\ 3)\\ \\ M\cup N=[-5,\ \ 5]\\ \\ M\cup N=[-1,\ \ 3)\\ \\ M\setminus N=[3,\ \ 5)\\ \\ N\setminus M=[-5,\ -1)[/tex]

2.

[tex]\it |2x-7|\leq3 \Rightarrow -3\leq2x-7\leq3|_{+7} \Rightarrow 4\leq2x\leq10|_{:2} \Rightarrow 2\leqx\leq5 \Rightarrow A=[2,\ \ 5]\\ \\ \\ \Big|\dfrac{2x+1}{9}\Big|\leq1 \Rightarrow -1\leq\ \dfrac{2x+1}{9}\leq1|_{\cdot9} \Rightarrow -9\leq2x+1\leq9|_{-1} \Rightarrow \\ \\ \\ \Rightarrow -10\leq 2x\leq8|_{:2} \Rightarrow -5\leq x\leq4 \Rightarrow B=[-5,\ \ 4][/tex]

[tex]\it A\cup B=[-5,\ \ 5]\\ \\ A\cap B=[2,\ \ 4]\\ \\ A\setminus B=(4,\ \ 5]\\ \\ B\setminus A=[-5,\ \ 2)[/tex]

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