[Title]
201(1)_ƕs
% ꂼ̖𓚂$\displaystyle $tꍇ́C@ON ܂1
% ꂼ̖𓚂$\displaystyle $tȂꍇ́COFF܂0
[displaystyle]
OFF

% 蕶
% Ȃ΁C[Level1]ɏ̂̂܂ܖ蕶ƂȂB
[Problem]
̖₢ɓB
% tHg̑傫B1`10C܂TeX̃R}hw肷B
% ftHǵC5i\normalsizej
% 1\tinyC 2\scriptsizeC3\footnotesizeC4\smallC 5\normalsize
% 6\largeC7\LargeC     8\LARGEC       9\hugeC 10\Huge
[FontSize]
5

% vAuɒǉpbP[Wt@Cw肷B
[usepackage]
\usepackage{color,amssymb}


% Level1̖BȉLevel7܂œlB
% 1sڂɂ͏ڍאݒ̃^CgB
% 2sڈȍ~ɖƂ̉𓚂B
% Ɖ𓚁C𓚂Ɩ͂PsďB
% vZߒꍇ́CƉ𓚂̊ԂɂPsԊuC
% ŏprocessƂsC̎̍svZߒĂB
[Level1]
P
̕ȂB\\
$2(x-3)=3(x+2)$

process
$2x-6=3x+6$

$x=-12$

̕ȂB\\
$4(x-3)=3(x-2)$

$x=6$

̕ȂB\\
$3(x-2)-5=-x+1$

$x=3$

̕ȂB\\
$5x-2(4x-3)=18$

$x=-4$

̕ȂB\\
$\displaystyle \frac{2x+1}{3}=\displaystyle \frac{1+x}{2}$

process
ӂ6\\
$2\left(2x+1 \right)=3\left(1+x \right)$

$x=1$

̕ȂB\\
$1-\displaystyle \frac{x-2}{6}=3-\displaystyle \frac{x}{2}$

process
ӂ6\\
$6-\left(x-2 \right)=18-3x$

$x=5$

̕ȂB\\
$\displaystyle \frac{1}{2}-\displaystyle \frac{4-x}{3}=\displaystyle \frac{5}{6}$

process
ӂ6\\
$3-2\left(4-x \right)=5$

$x=5$

̕ȂB\\
$\displaystyle \frac{6x+2}{3}-\displaystyle \frac{4x-4}{6}=1$

process
ӂ6\\
$2\left(6x+2 \right)-(4x-4)=6$

$x=-\displaystyle \frac{1}{4}$

̕ȂB\\
$2x-4=7x-(x-8)$

$x=-3$

̕ȂB\\
$2x-2\{x-(1-x)\}=3x-8$

process
$2x-2\{ 2x-1 \}=3x-8$

$x=2$

̕ȂB\\
$0.5\left(3-x \right)-4\left(0.3x+0.65\right)+7.9=0$

process
ӂ10\\
$5\left(3-x \right)-4\left(3x+6.5 \right)+79=0$\\
$15-5x-12x-26+79=0$

$x=4$

̕ȂB\\
$0.3\left(x-1.5\right)=0.2x+1$

process
ӂ10\\
$3\left(x-1.5 \right)=2x+10$

$x=14.5$

̕ȂB\\
$\displaystyle \frac{2}{3}x-\displaystyle \frac{1}{2}=\displaystyle \frac{1}{6}x+2$

process
ӂ6\\
$4x-3=x+12$

$x=5$

̕ȂB\\
$\displaystyle \frac{6x+2}{2}-\displaystyle \frac{4x-4}{6}=1$

process
ӂ6\\
$3\left(6x+2\right)-\left(4x-4\right)=6$

$x=-\displaystyle \frac{2}{7}$

̕ȂB\\
$2x+1=\displaystyle \frac{2}{3} x +\displaystyle \frac{7}{3}$

process
ӂ$3$ƁC\\
$6x+3=2x+7$

$x=1$

̕ȂB\\
$8-2x=-3\left( x-3 \right)+2\left( x-2 \right)$

process
$8-2x=-3x+9+2x-4$\\

$x=3$

̕ȂB\\
$\displaystyle \frac{7}{6} x+6=\displaystyle \frac{3}{4} x-4$

process
ӂ12ƁC\\
$14x+72=9x-48$

$x=-24$

̕ȂB\\
$\displaystyle \frac{3x+5}{4}=\displaystyle \frac{x+1}{2} +3$

process
ӂ4ƁC\\
$3x+5=2\left(x+1 \right)+12$\\
$3x+5=2x+14$

$x=9$

̕ȂB\\
$4x+3 \left( 2x-3 \right)=18x-13$

process
$4x+6x-9=18x-13$\\
$10x-9=18x-13$

$x=\displaystyle \frac{1}{2}$

̕ȂB\\
$5\left( x-5 \right)-2\left( x-3 \right)=11$

$x=10$

̕ȂB\\
$2\left( 6-7x \right)=1-9\left( x-1 \right)$

$x=\displaystyle\frac{2}{5}$

̕ȂB\\
$\displaystyle\frac{5}{6} x-2=\displaystyle\frac{1}{3} x+\displaystyle\frac{1}{2}$

process
ӂ6ƁC$5x-12=2x+3$

$x=5$

̕ȂB\\
$\displaystyle\frac{x+1}{2}-\displaystyle\frac{x-1}{4}=1$

process
ӂ4\\
$2\left( x+1 \right)-\left( x-1 \right)=4$

$x=1$

̕ȂB\\
$\displaystyle\frac{1}{4} x+\displaystyle\frac{2}{3}=\displaystyle\frac{1}{2} x-\displaystyle\frac{1}{3}$

process
ӂ12ƁC\\
$3x+8=6x-4$

$x=4$

̕ȂB\\
$0.2\left(x-3\right)=1$

process
ӂ10ƁC\\
$2\left(x-3\right)=10$

$x=8$

̕ȂB\\
$-0.5x+0.7\left(x+0.3 \right)=0.63$

process
ӂ10ƁC\\
$-5x+7\left(x+0.3 \right)=6.3$

$x=2.1$

̕ȂB\\
$x-1=\displaystyle\frac{3x-1}{6}-\displaystyle\frac{x+3}{4}$

process
ӂ12ƁC\\
$12x-12=2\left(3x-1\right)-3\left(x+3\right)$

$x=\displaystyle\frac{1}{9}$

̕ȂB\\
$0.03x+2=0.12x-0.07$

process
ӂ100\\
$3x+200=12x-7$

$x=23$

̕ȂB\\
$0.6\left( x+0.2 \right)-0.4x=-0.7$

process
ӂ10\\
$6\left(x+0.2 \right)-4x=-7$\\
$6x+1.2-4x=-7$

$x=-4.1$

̕ȂB\\
$\displaystyle\frac{x}{2}=x-1$

process
ӂ2\\
$x=2x-2$C$2=2x-x$

$x=2$

̕ȂB\\
$1=\displaystyle\frac{2x-3}{5}$

process
ӂ5\\
$5=2x-3$C$8=2x$

$x=4$

̕ȂB\\
$\displaystyle\frac{x}{3}-\displaystyle\frac{x-3}{4}=1$

process
ӂ12\\
$4x-3\left(x-3\right)=12$C$4x-3x+9=12$

$x=3$

̕ȂB\\
$5(x+1)=x-3$

$x=-2$

̕ȂB\\
$0.7x-5=0.9x+11$

$x=-80$

̕ȂB\\
$\displaystyle\frac{x+5}{2}=\displaystyle\frac{4x-5}{3}$

$x=5$

̕ȂB\\
$0.6x+3=x-\displaystyle\frac{1}{5}$

$x=8$

̕ȂB\\
$0.6x-0.4=0.9x-4.3$

process
$6x-4=9x-43$

$x=13$

̕ȂB\\
$\displaystyle\frac{x+3}{2}=\displaystyle\frac{3x-1}{5}$

$x=17$

̕ȂB\\
$\displaystyle\frac{x+2}{3}=\displaystyle\frac{x-1}{2}$

$x=7$

̕ȂB\\
$1.5x-3=1.2x-0.3$

process
$15x-30=12x-3$

$x=9$

̕ȂB\\
$3(4x-7)=-5(3-2x)$

process
$12x-21=-15+10x$

$x=3$









[Level2]
1s
̕sȂB\\
$0.3x+1 < 0.5x-0.2$

$x>6$

̕sȂB\\
$3(x+2)<5(x-2)$

$x>8$

̕sȂB\\
$-\displaystyle \frac{1}{3} x \ge 3$

$x \le -9$

̕sȂB\\
$3x-4 \le 6x+5$

$x \ge -3$

̕sȂB\\
$-\displaystyle \frac{1}{4} x <7$

$x>-28$

̕sȂB\\
$2\left(3x-5\right)>5x-9$

process
$6x-10>5x-9$

$x>1$

̕sȂB\\
$\displaystyle \frac{3x-1}{2} \geqq 3x+1$

process
ӂ2\\
$3x-1 \geqq 6x+2$C$-3\geqq 3x$

$x \leqq -1$

̕sȂB\\
$0.3x-2.9 \geqq -2x+4$

process
ӂ10\\
$3x-29 \geqq -20x+40$C$23x \geqq 69$

$x \geqq 3$

̕sȂB\\
$3\left(2x-5 \right)>5x-9$

process
$6x-15>5x-9$

$x > 6$

̕sȂB\\
$3\left(x+3 \right)<4\left(1-x\right)+12$

process
$3x+9<4-4x+12$C
$7x<7$

$x < 1$

̕sȂB\\
$\displaystyle \frac{x+2}{5}+\displaystyle \frac{x-1}{3} \leqq 1$

process
ӂ15\\
$3\left(x+2\right)+5\left(x-1 \right)\leqq 15$C\\
$3x+6+5x-5 \leqq 15$

$x \leqq \displaystyle \frac{7}{4}$

̕sȂB\\
$\displaystyle \frac{5x-9}{6}+\displaystyle \frac{3x+5}{2} > 2$

process
ӂ6\\
$5x-9+3\left(3x+5\right)>12$

$x > \displaystyle \frac{3}{7}$

̕sȂB\\
$\displaystyle \frac{x}{6}-2>\displaystyle \frac{2}{3} x+3$

process
ӂ6\\
$x-12>4x+18$C
$-30>3x$

$x<-10$

̕sȂB\\
$\displaystyle \frac{x}{6} < \displaystyle \frac{1}{2} + \displaystyle \frac{x}{2}$

process
ӂ6\\
$x<3+3x$C$-3<2x$

$x>-\displaystyle \frac{3}{2}$

̕sȂB\\
$\displaystyle \frac{x}{3}-\displaystyle \frac{1}{2}<\displaystyle \frac{x}{4}+\displaystyle \frac{1}{3}$

process
ӂ12\\
$4x-6<3x+4$

$x<10$

̕sȂB\\
$2 \left( x-3 \right)>3 \left( 2x-1 \right)$

process
$2x-6 > 6x-3$C$-3>4x$

$x<-\displaystyle \frac{3}{4}$

̕sȂB\\
$7 \left( x-2 \right)<-2\left( 3x+1 \right)$

process
$7x-14<-6x-2$

$x<\displaystyle \frac{12}{13}$

̕sȂB\\
$3x+8 \geqq 2\left( 5x+7 \right)+4$

process
$3x+8 \geqq 10x +14 +4$C\\
$-10 \geqq 7x$

$x \leqq -\displaystyle \frac{10}{7}$

̕sȂB\\
$2\left( x-3 \right)<5 \left( x-2 \right)+6$

process
$2x-6< 5x-10+6$C
$-2<3x$

$x>-\displaystyle \frac{2}{3}$

̕sȂB\\
$\displaystyle \frac{x-1}{2}>\displaystyle \frac{x+3}{3}$

process
ӂ6\\
$3 \left( x-1 \right)>2\left( x+3 \right)$C
$3x-3>2x+6$

$x>9$

̕sȂB\\
$\displaystyle \frac{x-5}{7}<\displaystyle \frac{x}{3}-2$

process
ӂ21\\
$3 \left( x-5 \right)<7x-2 \times 21$C
$3x-15<7x-42$

$x>\displaystyle \frac{27}{4}$

̕sȂB\\
$0.3x-5 \geqq 1-1.2x$

process
ӂ$10$\\
$3x-50 \geqq 10-12x$C
$15x \geqq 60$

$x \geqq 4$

̕sȂB\\
$\displaystyle \frac{x+1}{3}<\displaystyle \frac{x-4}{2}$

process
ӂ6ƁC\\
$2\left(x+1\right)<3\left(x-4\right)$C
$2x+2<3x-12$

$x>14$

̕sȂB\\
$x+5 \geqq \displaystyle \frac{1-x}{2}$

process
ӂ$2$ƁC\\
$2\left(x+5 \right) \geqq 1-x$ ,\ $2x+10 \geqq 1-x$\\
$3x \geqq -9$ 

$x \geqq -3$

̕sȂB\\
$\displaystyle \frac{1}{2}\,x>x-3$

process
ӂ2\\
$x>2x-6$C\ $\therefore 6>x$

$x<6$

̕sȂB\\
$0.4x+1.2>x$

process
10𗼕ӂɊ|ƁC\\
$4x+12>10x$C$12>6x$\\

$x<2$

̕sȂB\\
$\displaystyle \frac{5-x}{2} \geqq x+1$

process
ӂ2\\
$5-x \geqq 2\left(x+1 \right)$,\  $5-x \geqq 2x+2$\\
$5-2 \geqq 2x+x$ ,\ $3 \geqq 3x$

$x \leqq 1$

̕sȂB\\
$3-x \geqq \displaystyle\frac{x-1}{2}$

process
ӂ2\\
$6-2x \geqq x-1$C$7 \geqq 3x$

$x\leqq \displaystyle\frac{7}{3}$

̕sȂB\\
$x-0.5 > 1.4x+0.3$

process
ӂ10ƁC\\
$10x-5 > 14x+3$C$-8>4x$

$x < -2$

1sȂB\\
$5x-12>3\left(x-2 \right)$

process
$5x-12>3x-6$

$x>3$

1sȂB\\
$2x-3>\displaystyle\frac{5}{2}\, x$

process
$4x-6>5x$C$-6>5x-4x$

$x<-6$

1sȂB\\
$6x+14<\displaystyle\frac{2}{3}x+6$

process
ӂ3\\
$18x+42<2x+18$C$16x<-24$

$x<-\displaystyle\frac{3}{2}$

1sȂB\\
$\displaystyle\frac{x-4}{2}\geqq \displaystyle\frac{5+4x}{3}+1$

process
ӂ6\\
$3\left(x-4 \right)\geqq 2\left(5+4x\right)+6$\\
$3x-12 \geqq 16+8x$C$-28 \geqq 5x$

$x\leqq-\displaystyle\frac{28}{5}$

1sȂB\\
$1-2x<\displaystyle\frac{5+2x}{3}$

process
ӂ3\\
$3-6x<5+2x$C$-2<8x$

$x>-\displaystyle\frac{1}{4}$

1sȂB\\
$3 \left(x+1 \right)>x-3$

process
$3x+3>x-3$C\,$2x>-6$

$x>-3$

1sȂB\\
$5-2(x+3)<x+8$

process
$5-2x-6<x+8$C\,$-9<3x$

$x>-3$

1sȂB\\
$-4x+2(x-5)\geqq 6$

process
$-4x+2x-10\geqq 6$C\,$-16\geqq 2x$

$x\leqq -8$

1sȂB\\
$2(x-1)-3(x+2)<2$

process
$2x-2-3x-6<2$C\,$-x-8<2$C\,$-10<x$

$x>-10$

1sȂB\\
$\displaystyle\frac{2x-1}{6}>2-\displaystyle\frac{1-3x}{3}$

process
ӂ6\\
$2x-1>12-2\left(1-3x\right)$C\,$2x-1>12-2+6x$C\\
$-11>4x$

$x<-\displaystyle\frac{11}{4}$

1sȂB\\
$\displaystyle\frac{3}{4}\,x<\displaystyle\frac{3x-1}{6}+\displaystyle\frac{1}{2}$

process
ӂ12ƁC\\
$3\times 3x<2\left(3x-1 \right)+6$C\,$9x<6x-2+6$C\\
$3x<4$

$x<\displaystyle\frac{4}{3}$

1sȂB\\
$\displaystyle\frac{x+1}{2}<1-\displaystyle\frac{x-1}{3}$

process
ӂ6ƁC\\
$3\left(x+1\right)<6-2\left(x-1 \right)$C\,$3x+3<6-2x+2$C\\
$5x<5$

$x<1$

1sȂB\\
$3x-10>4\left(x-2\right)$

process
$3x-10>4x-8$C\,$-2>x$

$x<-2$

1sȂB\\
$1.6x-2.8>2.4x+2$

process
ӂ10\\
$16x-28>24x+20$C\,$-48>8x$

$x<-6$

1sȂB\\
$\displaystyle\frac{x+7}{3}-\displaystyle\frac{3(x+2)}{4}>1$

process
ӂ$12$ƁC\\
$4\left(x+7\right)-9\left(x+2\right)>12$C\\
$4x+28-9x-18>12$C\,$-5x+10>12$C\,$-2>5x$

$x<-\displaystyle\frac{2}{5}$

1sȂB\\
$0.7x-1.3\leqq 0.9x+0.3$

process
ӂ10\\
$7x-13\leqq 9x+3$C\,$-16\leqq 2x$

$x\geqq -8$

1sȂB\\
$3\left(x-2 \right)-4<2\left(x-1 \right)$

process
$3x-6-4<2x-2$

$x<8$

1sȂB\\
$\displaystyle\frac{1}{6}x-\displaystyle\frac{2}{3}\geqq \displaystyle\frac{1}{4}x$

process
ӂ12ƁC\\
$2x-8\geqq 3x$C\,$-8\geqq x$

$x\leqq -8$

1sȂB\\
$2\left(1-2x \right)>3x-1$

process
$2-4x>3x-1$C$3>7x$C$\displaystyle\frac{3}{7}>x$

$x<\displaystyle\frac{3}{7}$

1sȂB\\
$-\displaystyle\frac{x}{2}<x-3$

process
ӂ2ƁC\\
$-x<2x-6$C$6<3x$

$x>2$

1sȂB\\
$\displaystyle\frac{x}{2}>\displaystyle\frac{x}{3}+2$

process
ӂ6ƁC\\
$3x>2x+12$

$x>12$

1sȂB\\
$\displaystyle\frac{-x+2}{3}\geqq \displaystyle\frac{3x-1}{6}$

process
ӂ6ƁC\\
$2\left(-x+2\right)\geqq 3x-1$C
$-2x+4 \geqq 3x-1$C$5 \geqq 5x$

$x \leqq 1$

1sȂB\\
$\displaystyle\frac{3x+5}{2}< 5-\displaystyle\frac{x}{4}$

process
ӂ4ƁC\\
$2\left(3x+5\right)< 20-x$C
$6x+10 < 20-x$C$7x<10$

$x <\displaystyle\frac{10}{7}$

1sȂB\\
$2(2x-1)-7x+5>0$

$x<1$

1sȂB\\
$\displaystyle\frac{2}{3} x+\displaystyle\frac{1}{2}>x-1$

process
ӂ6ƁA\\
$4x+3>6x-6$C$9>2x$

$x<\displaystyle\frac{9}{2}$

ꎟs
$\displaystyle\frac{x+2}{3} \geqq \displaystyle\frac{3x-1}{2}$
ƁC̉͂ǂꂩB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,$x \geqq -1$~~~
\textcircled{\small 2}\,$x \leqq -1$~~~
\textcircled{\small 3}\,$x \geqq 1$~~~
\textcircled{\small 4}\,$x \leqq 1$~~~

process
ӂ6ƁC\\
$2\left(x+2 \right) \geqq 3\left(3x-1 \right)$\\
$2x+4 \geqq 9x-3$~~~~~~~~~~~$7 \geqq 7x$

\textcircled{\small 4}

ꎟs
$3x-3 \leqq 2\left( 2x-1 \right)$
ƁC̉͂ǂꂩB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,$x \leqq -1$~~~
\textcircled{\small 2}\,$x \geqq -1$~~~
\textcircled{\small 3}\,$x \leqq 1$~~~
\textcircled{\small 4}\,$x \geqq 1$~~~

process
$3x-3 \leqq 4x-2$\\
$2-3 \leqq x$~~~~~~~~$-1 \leqq x$

\textcircled{\small 2}

ꎟs
$3-x > 2\left( x+5 \right)$̉͂ǂꂩB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,$x > -\displaystyle\frac{7}{3}$~~~
\textcircled{\small 2}\,$x < -\displaystyle\frac{7}{3}$~~~
\textcircled{\small 3}\,$x > \displaystyle\frac{7}{3}$~~~
\textcircled{\small 4}\,$x < \displaystyle\frac{7}{3}$

process
$3-x>2x+10$~~~~~~~
$3-10 > 2x+x$~~~~~~~~
$-7 > 3x$

\textcircled{\small 2}

ꎟs
$x+1 > \displaystyle\frac{5x+8}{2}$ƁC
$\fbox{\,A\,}$łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,$x<-2$~~~
\textcircled{\small 2}\,$x>-2$~~~
\textcircled{\small 3}\,$x<2$~~~
\textcircled{\small 4}\,$x>2$

process
$2x+2 > 5x+8$\\
$-6> 3x$~~~$-2>x$

\textcircled{\small 1}

1sȂB\\
$\displaystyle\frac{2x+1}{3}\geqq x-\displaystyle\frac{x-1}{4}$

process
$4(2x+1)\geqq 12-3(x-1)$\\
$8x+4\geqq 12-3x+3$

$x\geqq 1$

1sȂB\\
$1-2(x+3)<3x$

process
$1-2x-6<3x$\\

$x>-1$

1sB\\
$0.3(x+1)>0.4x+1$

process
$0.3x+0.3>0.4x+1$\\
$-0.7>0.1x$

$x<-7$

1sB\\
$\displaystyle \frac{2x-5}{3} < \displaystyle \frac{-x+7}{2}$

process
$2(2x-5) < 3(-x+7)$C\\
$4x-10<-3x+21$C$x<\displaystyle \frac{31}{7}$

$x<\displaystyle \frac{31}{7}$

1sB\\
$\displaystyle\frac{1}{4}(3x-8)\leqq 2x-3$

process
$3x-8\leqq 8x-12$

$x\geqq \displaystyle\frac{4}{5}$

1sB\\
$\displaystyle\frac{x-3}{3}\leqq \displaystyle\frac{2x-1}{5}$

process
$5(x-3)\leqq 3(2x-1)$\\
$5x-15\leqq 6x-3$

$x\geqq -12$

1sB\\
$\displaystyle\frac{3}{4}x+ \displaystyle\frac{1}{2} < \displaystyle\frac{2}{3}(x+1)$

process
$3\times 3x+6<4\times 2(x+1)$\\
$9x+6<8x+8$

$x< 2$

1s$\displaystyle\frac{3x-1}{5}\leqq x+3$ƁC
̉\fbox{\bf\, A \,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,$x \geqq 8$~~~
\textcircled{\small 2}\,$x \leqq 8$~~~
\textcircled{\small 3}\,$x \geqq -8$~~~
\textcircled{\small 4}\,$x \leqq -8$

\textcircled{\small 3}

s
$-0.7x-0.4\geqq -0.2x+1.6$
ƁC̉͂ǂꂩB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,$x\leqq 4$~~~
\textcircled{\small 2}\,$x\geqq 4$~~~
\textcircled{\small 3}\,$x\leqq -4$~~~
\textcircled{\small 4}\,$x\geqq -4$

process
$-7x-4\geqq -2x+16$~~~$-20 \geqq 5x$

\textcircled{\small 3}

s
$x+6>-2x-12$̉ƂāĈ͂ǂꂩB
\textcircled{\small 1}$\sim$\textcircled{\small 6}
̒1IсC̋L𓚂B\\
\textcircled{\small 1}\,$x>6$~~~
\textcircled{\small 2}\,$x<-6$~~~
\textcircled{\small 3}\,$x<6$\\
\textcircled{\small 4}\,$x>-6$~~~
\textcircled{\small 5}\,$x>-3$~~~
\textcircled{\small 6}\,$x<-3$

\textcircled{\small 4}

ꎟs
$2(1+x)+7 \leqq 3(x-1)$ƁC̉\fbox{\hspace{4pt} A \hspace{4pt}}
łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂琳̂IׁB\\
\textcircled{\small 1}\,$x\geqq 12$~~~
\textcircled{\small 2}\,
$x \leqq 12$~~~
\textcircled{\small 3}\,$x\geqq -12$~~~
\textcircled{\small 4}\,$x\leqq -12$

process
$2+2x+7 \leqq 3x-3$

\textcircled{\small 1}

1s$0.4x>x+1.2$ƁC̉
\fbox{\bf\hspace{4pt} A \hspace{4pt}}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,$x<4$~~~
\textcircled{\small 2}\,$x>4$~~~
\textcircled{\small 3}\,$x<-2$~~~
\textcircled{\small 4}\,$x>-2$

\textcircled{\small 3}









[Level3]
A
̘AȂB\\
$\left\{ 
\begin{array}{l}
2x+3y=1 \\
3x-4y=10
\end{array} \right.$

process
$(1) \times 4: 8x+12y=4 $\\
$(2) \times 3: 9x-12y=30$

$x=2, y=-1$

̘AȂB\\
$\left\{ 
\begin{array}{l}
5x+y=8 \\
3x-4y=14
\end{array} \right.$

process
$(1) \times 4: 20x+4y=32$ \\
$(2) : 3x-4y=14$

$x=2, y=-2$

̘AȂB\\
$\left\{ 
\begin{array}{l}
3x-y=10 \\
2x+3y=3
\end{array} \right.$

process
$(1) \times 3: 9x-3y=30$ \\
$(2) : 2x+3y=3$

$x=3, y=-1$

̘AȂB\\
$\left\{ 
\begin{array}{l}
2x+y=7 \\
5x+3y=19
\end{array} \right.$

process
$(1) \times (-3): -6x-3y=-21$ \\
$(2) : 5x+3y=19$

$x=2, y=3$

̘AȂB\\
$\left\{ 
\begin{array}{l}
3x+y=7 \\
2x-3y=12
\end{array} \right.$

process
$(1) \times 3: 9x+3y=21$ \\
$(2) : 2x-3y=12$

$x=3, y=-2$

̘AȂB\\
$\left\{
\begin{array}{l}
x+y=5 \\
4x-3y=13
\end{array} \right.$

process
$(1) \times 3: 3x+3y=15$ \\
$(2) : 4x-3y=13$

$x=4, y=1$

̘AȂB\\
$\left\{ 
\begin{array}{l}
x+2y=5 \\
x+3y=9
\end{array} \right.$

process
$(1)  \times -1: -x-2y=-5 $\\
$(2) \,\,\,: x+3y=9$

$x=-3, y=4$

̘AȂB\\
$\left\{ 
\begin{array}{l}
5x+3y=1 \\
2x-4y=16
\end{array} \right.$

process
$(1) \times 4: 20x+12y=4 $\\
$(2) \times 3: 6x-12y=48$

$x=2, y=-3$

̘AȂB\\
$\left\{ 
\begin{array}{l}
3x-2y=-7 \\
2x+3y=4
\end{array} \right.$

process
$(1) \times 3: 9x-6y=-21 $\\
$(2) \times 2: 4x+6y=8$

$x=-1, y=2$

̘AȂB\\
$\left\{ 
\begin{array}{l}
8x-5y=17 \\
3x-4y=0
\end{array} \right.$

process
$(1) \times 4: 32x-20y=68 $\\
$(2) \times (-5): -15x+20y=0$

$x=4, y=3$

̘AȂB\\
$\left\{ 
\begin{array}{l}
3x+y=-4x+3y+3 \\
5x-y=3x+2y+13
\end{array} \right.$

process
$\left\{ 
\begin{array}{l}
7x-2y=3 \\
2x-3y=13
\end{array} \right.$ \\
$(1) \times 3: 21x-6y=9 $\\
$(2) \times (-2): -4x+6y=-26$

$x=-1, y=-5$

̘AȂB\\
$\left\{ 
\begin{array}{l}
x+y=9 \\
x+2y=12
\end{array} \right.$

process
$(1) \times (-1): -x-y=-9 $\\
$(2) : x+2y=12$

$x=6, y=3$

̘AȂB\\
$\left\{ 
\begin{array}{l}
3x-2y=-1 \\
x+2y=5
\end{array} \right.$

$x=1, y=2$

̘AȂB\\
$\left\{ 
\begin{array}{l}
4x+y=1 \\
3x-2y=9
\end{array} \right.$

process
$(1) \times 2: 8x+2y=2$ \\
$(2) : 3x-2y=9$

$x=1, y=-3$

̘AȂB\\
$\left\{ 
\begin{array}{l}
x-y=-5 \\
x+2y=1
\end{array} \right.$

process
$(1) \times 2: 2x-2y=-10$ \\
$(2) : x+2y=1$

$x=-3, y=2$

̘AȂB\\
$\left\{ 
\begin{array}{l}
y=3x-8 \\
2x+y=7
\end{array} \right.$

process
$(1) : y=3x-8$
$(2) \times (-1): -2x-y=-7 $\\

$x=3, y=1$

̘AȂB\\
$\left\{ 
\begin{array}{l}
4x+3y=-2 \\
3x-2y=7
\end{array} \right.$

process
$(1) \times 2: 8x+6y=-4 $\\
$(2) \times 3: 9x-6y=21$

$x=1, y=-2$

̘AȂB\\
$\left\{ 
\begin{array}{l}
2x+y=7 \\
x-y=2
\end{array} \right.$

$x=3, y=1$

̘AȂB\\
$\left\{ 
\begin{array}{l}
3x+2y=-1 \\
x-y=3
\end{array} \right.$

process
$(1) : 3x+2y=-1 $\\
$(2) \times 2: 2x-2y=6$

$x=1, y=-2$

̘AȂB\\
$\left\{ 
\begin{array}{l}
5x+3y=4 \\
7x+2y=-1
\end{array} \right.$

process
$(1) \times -2: -10x-6y=-8 $\\
$(2) \times 3: 21x+6y=-3$

$x=-1Cy=3$

̘AȂB\\
$\left\{ 
\begin{array}{l}
5x+3y=1 \\
3x-4y=18
\end{array} \right.$

process
$(1) \times 4: 20x+12y=4 $\\
$(2) \times 3: 9x-12y=54$

$x=2Cy=-3$

̘AȂB\\
$\left\{ 
\begin{array}{l}
x-3y=-13 \\
2x+y=2
\end{array} \right.$

$x=-1, y=4$

̘AȂB\\
$\left\{ 
\begin{array}{l}
3x+2y=5 \\
2x+y=-1
\end{array} \right.$

$x=-7, y=13$





[Level4]
Ảp
̘Ả$x=-1Cy=-2$łƂC$aCb$̒l߂ȂB\\
$\left\{ 
\begin{array}{l}
2x+y=a \\
3x-y=a-b
\end{array} \right.$

process
$x=-1Cy=-2$^ɑƁC\\
$2 \times (-1) -2=a$\\
$3 \times (-1)-(-2)=a-b$\\
$ a=-4\,c(1)$\\
$a-b=-1\,c(2)$

$a=-4, b=-3$

̘AȂB\\
$\left\{ 
\begin{array}{l}
\displaystyle \frac{3+4x}{3}+2y=2 \\
x-2=\displaystyle \frac{-2y+1}{4}
\end{array} \right.$

process
$(1) \times 3: 3+4x+6y=6 $\\
$(2) \times 4: 4x-8=-2y+1$\\
$ (1):4x+6y=3$\\
$\,(2):-4x-2y=-9$

$x=3, y=-\displaystyle \frac{3}{2}$







[Level5]
As
̘AsȂB\\
$\left\{ 
\begin{array}{l}
x-11 \leqq 3x-9 \\
4x-8 \leqq 7-x
\end{array} \right.$

process
(1)$-1 \leqq x$C(2)$x \leqq 3$

$-1 \leqq x \leqq 3$

̘AsȂB\\
$\left\{ 
\begin{array}{l}
2x+7 < 9 \\
5x+18 > 3
\end{array} \right.$

process
(1)$x<1$C(2)$x>-3$

$-3 < x <1$

̘AsȂB\\
$\left\{ 
\begin{array}{l}
-3x+5 > -1 \\
-4x+2 < 10
\end{array} \right.$

process
(1)$x<2$C(2)$-2<x$

$-2<x<2$

̘AsȂB\\
$\left\{ 
\begin{array}{l}
5x-2 \geqq 8 \\
3x-6 > 9
\end{array} \right.$

process
(1)$x \geqq 2$C(2)$x>5$

$x>5$

̘AsȂB\\
$\left\{ 
\begin{array}{l}
2x-13 < -3x+7 \\
-3x+2 \leqq -x+2
\end{array} \right.$

process
(1)$x < 4$C(2)$0 \leqq x$

$0 \leqq x <4$

̘AsȂB\\
$\left\{ 
\begin{array}{l}
-1+2x \leqq -9 \\
3-4x > 11
\end{array} \right.$

process
(1)$x \leqq -4$C(2)$x < -2$

$x \leqq -4$

̘AsȂB\\
$\left\{ 
\begin{array}{l}
4x-3 \leqq 7x+15 \\
5x-2 < 3x+4
\end{array} \right.$

process
(1)$x \geqq -6$C(2)$x < 3$

$-6 \leqq x < 3$

̘AsȂB\\
$\left\{ 
\begin{array}{l}
3x-2 < x+6 \\
5x-6 > 3x-10
\end{array} \right.$

process
(1)$x < 4$C(2)$x > -2$

$-2 < x < 4$

̘AsȂB\\
$\left\{ 
\begin{array}{l}
4x-6 \leqq x+9 \\
5x+12 < 2x+3
\end{array} \right.$

process
(1)$x \leqq 5$C(2)$x < -3$

$x < -3$

̘AsȂB\\
$\left\{ 
\begin{array}{l}
4x-2 < 2x \\
6-2x \geqq -3x
\end{array} \right.$

process
(1)$x < 1$C(2)$x \geqq -6$

$-6 \leqq x < 1$

̘AsȂB\\
$\left\{ 
\begin{array}{l}
5-3x \leqq 12 \\
-2x+4 > -5
\end{array} \right.$

process
(1)$x \geqq -\displaystyle \frac{7}{3}$C(2)$x < \displaystyle \frac{9}{2}$

$-\displaystyle \frac{7}{3} \leqq x < \displaystyle \frac{9}{2}$

̘AsƁC̉\fbox{\,\bf A\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB
$\left\{ 
\begin{array}{l}
x>2 \\
x+3\leqq 3x-7
\end{array} \right.$@\\
\textcircled{\small 1}\,$2<x\leqq 5$~~~
\textcircled{\small 2}\,$x\geqq 5$~~~
\textcircled{\small 3}\,$x< 2$~~~
\textcircled{\small 4}\,$2\leqq x< 5$

process
(1)$2 < x$C(2)$5\leqq x$

\textcircled{\small 2}






[Level6]








[Level7]



[Level8]


[EOF]
% t@C̍Ōɂ
