a)
2(x+1)+3(2+x)\geq-12
2x+2+6+3x\geq-12
5x+8\geq-12
5x\geq-12-8
5x\geq-20|:5
x\geq-4
x\in\langle-4;+\infty)
b)
4(x-5)-2(x-1)<13
4x-20-2x+2<13
2x-18<13
2x<13+18
2x<31|:2
x<\frac{31}{2}
x<15\frac{1}{2}
x\in (-\infty;15\frac{1}{2})
c)
3x-2[2x-3(x+5)]\geq6x-11
3x-2(2x-3x-15)\geq6x-11
3x-2(-x-15)\geq6x-11
3x+2x+30\geq6x-11
5x-6x\geq-11-30
-x\geq-41|*(-1) zmiana znaku
x\leq41
x\in (-\infty;41\rangle
d)
3(x-4)\leq24-2(x+3)
3x-12\leq24-2x-6
3x-12\leq18-2x
3x+2x\leq18+12
5x\leq30|:5
x\leq6
x\in(-\infty;6\rangle
e)
1-6x<5x-2[4(3x-1)-3x]
1-6x<5x-2(12x-4-3x)
1-6x<5x-2(9x-4)
1-6x<5x-18x+8
1-6x<-13x+8
-6x+13x<8-1
7x<7|:7
x<1
x\in(-\infty;1)