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so now we need to consider the line y=4. this will be a horizontal line which passes through y=4.

the horizontal line could intersect the curve at some points. e.g.:
|dw:1322436287068:dw|

now since our inequality is y>=4, we need to draw a solid line at the places where y=4.

|dw:1322436426127:dw|

but what about the shaded region?

sorry - my explanation went a bit hay wire above!

what I should have said is lets say we have an inequality of the form y>=f(x)

lol it's okay take your time :)

now, on the curve y=f(x), we know it satisfies the inequality - so we make the line solid

below the curve y=f(x) does NOT satisfy the inequality as there we have y

above the curve y=f(x) DOES satisfy the inequality, so we include that region by shading it in

for shading it in, how do you know it satisfies the inequality?

|dw:1322436711384:dw|

does the diagram make sense?

not really :(

I have taken some point x=x1 (which is represented by the vertical line)
where this vertical line crosses the curve y=f(x), we know y=f(x1)
above that point of intersection, we know y>f(x1)
below that point of intersection, we know y

thanks :)

np - sorry for the confusion at the beginning :-)