Question

Помогите решить уравнения!
7(x-1)=4x

2(-x-5)=-(x+1)

-(3x-2)=-x

3(x+2)=2(x-1)

-5(3-x)=6(x+1)

4(0.5x-3)-6(0,3x-4)=12.24

0.4(1-2y)=3(0.3y-5)+10.3

Answer 1

$1) 7~\left(x-1\right)=4~x\\7~x-7=4~x\\7~x-7-4~x=4~x-4~x\\3~x-7=4~x-4~x\\3~x-7=0\\3~x-7+7=0+7\\3~x=0+7\\3~x=7\\\frac{3~x}{3}=\frac{7}{3}\\x=\frac{7}{3}$

$2) 2~\left(-x-5\right)=-\left(x+1\right)\\-2~x-10=-\left(x+1\right)\\-2~x-10=-x-1\\-2~x-10+x=-x-1+x\\-x-10=-x-1+x\\-x-10=-1\\-x-10+10=-1+10\\-x=-1+10\\-x=9\\-x~-1=9~-1\\x=9~-1\\x=-9$

$3) -\left(3~x-2\right)=-x\\-3~x+2=-x\\-3~x+2+x=-x+x\\-2~x+2=-x+x\\-2~x+2=0\\-2~x+2-2=0-2\\-2~x=0-2\\-2~x=-2\\\frac{-2~x}{-2}=\frac{-2}{-2}\\x=\frac{-2}{-2}\\x=1$

$4) 3~\left(x+2\right)=2~\left(x-1\right)\\3~x+6=2~\left(x-1\right)\\3~x+6=2~x-2\\3~x+6-2~x=2~x-2-2~x\\x+6=2~x-2-2~x\\x+6=-2\\x+6-6=-2-6\\x=-2-6\\x=-8$

$5)-5~\left(3-x\right)=6~\left(x+1\right)\\-15+5~x=6~\left(x+1\right)\\-15+5~x=6~x+6\\-15+5~x-6~x=6~x+6-6~x\\-x-15=6~x+6-6~x\\-x-15=6\\-x-15+15=6+15\\-x=6+15\\-x=21\\-x~-1=21~-1\\x=21~-1\\x=-21$

$6)4\left(0.5x-3\right)-6\left(0.3x-4\right)=12.24\\0.2x+12=12.24\\0.2x+12-12=12.24-12\\0.2x=0.24\\\frac{0.2x}{0.2}=\frac{0.24}{0.2}\\x=1.2$

$7) 0.4~\left(1-2~y\right)=3~\left(0.3~y-5\right)+10.3\\0.4-0.8~y=3~\left(0.3~y-5\right)+10.3\\0.4-0.8~y=0.9~y-4.7\\0.4-0.8~y-0.9~y=0.9~y-4.7-0.9~y\\-1.7~y+0.4=0.9~y-4.7-0.9~y\\-1.7~y+0.4=-4.7\\-1.7~y+0.4-0.4=-4.7-0.4\\-1.7~y=-4.7-0.4\\-1.7~y=-5.1\\\frac{-1.7~y}{-1.7}=\frac{-5.1}{-1.7}\\y=\frac{-5.1}{-1.7}\\y=3$