negative 2 absolute sign h-2 absolute sign is greater than negative 2

Good try sasflower but you have made a couple of little mistakes. I'll give you thumbs up for your good effort :)

$$\\-2|h-2|\ge2\\\\
$Divide both sides by -2 but remember that when you divide or multiply by a negative number you must turn the inequality around$\\\\
|h-2|\le1\\\\
-1\le h-2\le1\\\\
1\le h \le 3$$

2 l h-2 l > -2

first divide by 2 on both sides

l h-2 l > -2

now seperate it into 2 inequalities

h-2 > -2  h-2 < .....

this absolute value inequality cannot seperate into 2 inequalities so the answer is

no solution