Question

Rezolvati in Z ecuatiile:a)2(x+1)>si egal ca -8;b)3(x+6)< si egal ca-9;c)5+2(x-1)>si egal ca 7;d)9-3(x+2)<-3;e)10<3(x+8)+1;f)-8*(-x)+4>si egal -20;g)12+3*(-2x)>0;h)(-4x):2+6>-4;i)(-9x):(-3)+2si egal ca 3; c)2<|x|si egal ca -3;d)|x|>0;f)|x|-5;p)|2x+2|<0 ex 10 rezolvati ecuatiile in Z.a)3x-10=-25;b)-105=x+25;c)5(x+4)-81=-106;d)5(2-x)+92=17;e)8-2(4-x)=-18;f)40-3(1-x)=-14;g)|3x-1|=10;h)5|2x+3|=35 ajutatima va rog

Answer 1

$a).2(x+1) \geq -8 \\ 2x+2 \geq -8 \\ 2x \geq -8-2 \\ 2x \geq -10 \\ x \geq -5 \\ b).3(x+6) \leq -9 \\ 3x+18 \leq -9 \\ 3x \leq -9-18 \\ 3x \leq -27 \\ x \leq -9 \\ c).5+2(x-1) \geq 7 \\ 5+2x-2 \geq 7 \\ 2x \geq 7-5+2 \\ 2x \geq 4 \\ x \geq 2$
$d).9-3(x+2)\ \textless \ -3 \\ 9-3x-6\ \textless \ -3 \\ -3x\ \textless \ -3-9+6 \\ -3x\ \textless \ -6 \\ x\ \textgreater \ 2 \\ e).10\ \textless \ 3(x+8)+1 \\ 10\ \textless \ 3x+24+1 \\ -3x\ \textless \ 24+1-10 \\ -3x\ \textless \ 15 \\ x\ \textgreater \ -5$
$f).-8*(-x)+4 \geq -20 \\ 8x+4 \geq -20 \\ 8x \geq -20-4 \\ 8x \geq -24 \\ x \geq -3 \\ g).12+3*(-2x)\ \textgreater \ 0 \\ 12-6x\ \textgreater \ 0 \\ -6x\ \textgreater \ 0-12 \\ -6x\ \textgreater \ -12 \\ x\ \textless \ 2 \\ h).(-4x):2+6\ \textgreater \ -4 \\ -2x+6\ \textgreater \ -4 \\ -2x\ \textgreater \ -4-6 \\ -2x\ \textgreater \ -10 \\ x\ \textless \ 5$
$i).(-9x):(-3)+2=3 \\ 3x+2=3 \\ 3x=3-2 \\ 3x=1 \\ x= \frac{1}{3} \\ d).|x|\ \textgreater \ 0 \\ x\ \textgreater \ 0;x\ \textless \ 0 \\ p).|2x+2|\ \textless \ 0 -Fals \\ a).3x-10=-25 \\ 3x=-25+10 \\ 3x=-15 \\ x=-5$
$b).-105=x+25 \\ -x=25+105 \\ -x=130 \\ x=-130 \\ c).5(x+4)-81=-106 \\ 5x+20-81=-106 \\ 5x=-106-20+81 \\ 5x=-45 \\ x=-9 \\ d).5(2-x)+92=17 \\ 10-5x+92=17 \\ -5x=17-10-92 \\ -5x=-85 \\ x=17$
$e).8-2(4-x)=-18 \\ 8-8+2x=-18 \\ 2x=-18-8+8 \\ 2x=-18 \\ x=-9 \\ f).40-3(1-x)=-14 \\ 40-3+3x=-14 \\ 3x=-14-40+3 \\ 3x=-51 \\ x=-17$
$g).|3x-1|=10 \\ 3x-1=10 \\ 3x=11 \\ x= \frac{11}{3} \\ 3x-1=-10 \\ 3x=-9 \\ x=-3$
$h).5|2x+3|=35 \\ |2x+3|=35:5 \\ |2x+3|=7 \\ 2x+3=7 \\ 2x=4 \\ x=2 \\ 2x+3=-7 \\ 2x=-10 \\ x=-5$