`a)\ (x-2)/5+3

$3\left(x-2\right)+45<5\left(x+2\right)-15\mid +15$

$3\left(x-2\right)+60<5\left(x+2\right)$

$3x-6+60<5x+10$

$3x+54<5x+10\mid -3x$

$54<2x+10\mid -10$ $54<2x+10\mid -10$

$44<2x\mid :2$

`\ \ \ 22

$x>22$

 

$b)\left(x+1\right)\left(x+2\right)\le \left(x+5\right)\left(x+6\right)$

$x^2+2x+x+2\le x^2+6x+5x+30$

$x^2+3x+2\le x^2+11x+30\mid -x^2$

$3x+2\le 11x+30\mid -3x$

$2\le 8x+30\mid -30$

$-28\le 8x$

$8x\ge -28\mid :8$

$x\ge -\frac{28}{8}$

$x\ge -\frac{7}{2}$

$x\ge -3\frac{1}{2}$

 

$c)\frac{1}{3}x+\frac{1}{6}\left(2x-12\right)\ge \frac{1}{2}x\mid \cdot 6$

$2x+2x-12\ge 3x$

$4x-12\ge 3x\mid -3x$

$x-12\ge 0\mid +12$

$x\ge 12$

 

$d)\left(x-5\right)\left(x+5\right)>{\left(x-5\right)}^2-25$

$x^2-25>x^2-10x+25-25$

$x^2-25>x^2-10x\mid -x^2$

$-25>-10x$

`\ \ \ -10x

$x>2,5$