Question

Rezolvati urmatoarele inecuatii unde x apartine Z:a) 5(x-8)>-3x
b)3(4-x)mai mic sau egal decat -7x
c)8+(x-7)mai mare sau egal decat-6x
d)4(2x-5)<-2x
e)8(15-2x)>4x
f)9(7-3x)mai mare sau egal decat -6x
Va rog ajutor!!

Answer 1

a)5x-40>-3x
5x+3x>40
8x>40
x>5
x€(5,infinit)
b)12-3x<=-7x
-3x+7x<=-12
4x<=-12
x<=-3
x€(-infinit,-3]
c)8+x-7>=-6x
x+6x>=7-8
7x>=-1
x>=-1/7
-1/7 este rațional
x€(-1/7;infinit)
cred că ai scris greșit,asta doreai
8x+6x>=56
14x>=56
x>=4
x€[4;infinit)
e)120-16x>4x
-20x>-120 |(-1)
20x<120
x<6
x€(-infinit,6)
f)63-27x>=-6x
-27x+6x>=-63 |(-1)
-21x>=-63 |(-1)
x<=3
x€(-infinit,3]

Answer 2

[tex]\it \ c)\ 8(x-7) \geq -6x \Rightarrow 8x-56 \geq -6x \Rightarrow 8x+6x\geq56 \Rightarrow \\ \\ \Rightarrow 14x \geq 56 \Rightarrow x \geq 56:14 \Rightarrow x \geq 4 \Rightarrow x \in \{4,\ 5,\ 6,\ ...\}[/tex]


[tex]\it d) \ 4(2x-5)\ \textless \ -2x \Rightarrow 8x-20\ \textless \ -2x \Rightarrow 8x+2x\ \textless \ 20 \Rightarrow \\ \\ \Rightarrow 10x\ \textless \ 20 \Rightarrow x\ \textless \ 20:2 \Rightarrow x\ \textless \ 2\Rightarrow x\in \{ ... -3,\ -2,\ -1,\ 0, 1\} \\ \\ \\ e) \ 8(15-2x)\ \textgreater \ 4x \Rightarrow 120-16x\ \textgreater \ 4x \Rightarrow 120\ \textgreater \ 4x +16x \Rightarrow \\ \\ \Rightarrow 120\ \textgreater \ 20x \Rightarrow 20x \ \textless \ 120 \Rightarrow x \ \textless \ 120:20 \Rightarrow x\ \textless \ 6 \Rightarrow x \in \{... 3 \ 4,\ 5\}[/tex]