Question

Va tog ajutor!!! Dau coroanaaaaa!!!!!

Answer 1

1.

$\it a)\ \ 3x+-15|_{:3} \Rightarrow x=-5\\ \\ b)\ \ 6x+7=31|_{-7} \Rightarrow 6x=24|_{:6} \Rightarrow x=4\\ \\ c)\ \ 4x+4=6x-7 \Rightarrow 3+7=6x-4x \Rightarrow 4=2x \Rightarrow x=2\\ \\ d)\ \ x-(2-x)=14 \Rightarrow x-2+x=14 \Rightarrow |_{+2} \Rightarrow 2x=12 \Rightarrow x=6\\ \\ e)\ \ \ |x+2|=3 \Rightarrow x+2=\pm3 \Rightarrow x+2\in\{-3,\ 3\}|_{-2} \Rightarrow x\in\{-5,\ 1\}$

2.

$\it a)\ x+2\geq5|_{-2} \Rightarrow x\geq3\ \stackrel{x\in\mathbb{Z}}{\Longrightarrow}\ x\in\{3,\ \ 4,\ \ 5,\ ...\}\\ \\ \\ b)\ -1 < x+1 < 6|_{-1} \Rightarrow -2 < x < 5\ \stackrel{x\in\mathbb{Z}}{\Longrightarrow}\ x\in\{-1,\ 0,\ 1,\ 2,\ 3,\ 4 \}$

3.

a)

$\it Not\breve am \ primul \ dintre \ numere \ cu \ a\ .\ \ Suma\ se\ scrie:\\ \\ a+a+1+a+2+a+3+a+4+a+5+a+6=7 \Rightarrow 7a+\dfrac{6\cdot7}{2}=7 \Rightarrow \\ \\ \\ \Rightarrow 7a+21=7|_{:7} \Rightarrow a+3=1|_{-3} \Rightarrow a=-2\\ \\ \\ Numerele\ \ cerute\ \ sunt:\ -2,\ \ -1,\ \ 0,\ \ 1,\ \ 2,\ \ 3,\ \ 4\ .$

b)

$\it Not\breve am\ \ num\breve arul\ \ cerut\ \ cu\ \ x\ .\\ \\ 3x+(-5)=x+(-3) \Rightarrow 3x-5=x-3 \Rightarrow 3x-x=-3+5 \Rightarrow 2x=2 \Rightarrow x=1$

c)

Notăm:

 c = numărul răspunsurilor corecte;

 90 - c = numărul  răspunsurilor  greșite .

$\it 3c-1\cdot(90-c)=170 \Rightarrow 3c-90+c=170|_{+90} \Rightarrow 4c=260|_{:4} \Rightarrow c=65$