For this problem, the " x " is -8 (first coordinate of the point).
So, we compare -8 in the left side with -7 in the right side of this hypothetical inequality,
and we see the inequality is valid.
At this point, the exercise is complete.
It's often puzzling to students when they are given an x and a y to substitute
and there is only one variable, (in this case x), and no place to substitute the
y-value of -1. It makes one wonder, "what am I going to do with y-value of -1?"
It doesn't seem right to students just to ignore the y-value.
The way I always explained this was to add a zero term in the missing variable,
in this case add " 0y ".
Think of
as if it were written
This did not change the inequality. Now there is a place to
substitute the y-value of -1
-8 is less than -7, so it's less than or equal -7.
And so the point (-8, -1) does satisfy the inequality x ≤ -7
Hope this lets you understand that you didn't just throw the
y-value of -1 away, but actually substituted it!
Edwin
