What is a good rule to understand how inequity shading works? I am learning mathematics for my upcoming IGCSE exams and we have a topic of Inequality where we are sometimes asked to 1) solve some inequality equation 2) shade a region that all the already given inequalities satisfy 3) derive 2-3 inequalities that define an already-shaded region. The last part is where I have some troubles. I want to show two problems of such type that I am having trouble with.

For this question, the answers are:
x<=3
y>=6-2x
y<=5+x
By the looks of it, it is my understanding that if the region shaded is below or behind the line then we use the "<=" or "<" sign. Because for the question, x<=3 was an answer since the shaded parts were behind x=3. And that if the region shaded is above or in front of the line, then we use the ">=" or ">" sign. For example, y>=6-2x was an answer since the shaded parts were above y=6-2x. This is my understand and I can be wrong on this one, it is my request to correct me if I am.
But I also encountered another question which seemed to contradict this point.

For this question, the answers were:
x>=0
x+y<=5
x-y<=5
So here, according to what I understand, x>=0 is correct since the shaded region is in front of it. And, x+y<=5 is also correct since the shaded region was below it. But why is x-y<=5 the third answer instead of x-y>=5? From the question, is it clear that the shaded region is above x-y=5 line so shouldn't the third answer be x-y>=5? Why is it x-y<=5?
This is my question and I hope I was able to clearly state the trouble that I am having. It will be much appreciated if anyone can help me with when to use ">=" and when to use "<=".
 A: Rules that always work are:
If the equation of the line is in the form $x = ay + b,$
then the region $x \leq ay + b$ will be on the left of the line and the
region $x \geq ay + b$ will be on the right of the line.
If the equation of the line is in the form $y = ax + b,$
then the region $y \leq ax + b$ will be below the line and the
region $y \geq ax + b$ will be above the line.
These rules work because the lesser value of $x$ is always on the left of the greater value of $x$, and the lesser value of $y$ is always below the greater value of $y.$
But these rules do not always work when you mix $x$ and $y$ together on the same side of an inequality.
In the case of $x - y \leq 5,$ the left hand side can become less if you decrease $x$
(moving to the left), but it can also become less if you increase $y$
(moving upward).
To disambiguate this, you can rewrite the inequality with just one variable on each side, for example,
$x \leq y + 5$ is completely equivalent to $x - y \leq 5,$
but because it is in the form $x \leq ay+b$ we see that the shaded region must be on the left side of the line, which it is.

Another way to figure out which side to shade is:
Pick a point that is not on the line.
Take the $x$ and $y$ coordinates of that point and plug them into the inequality.
Is the inequality true with these values plugged in?
If so, the point you chose is on the side where the shading should be.
If not, the shading should be on the opposite side.
