Question

graph the inequality on a number line -x^2+2x<-3

Answer 1

Multiply through by -1 and reverse the inequality sign (just to make it nicer):
\[ x^2-2x>3 \]
Put this in completed square form
\[ (x-1)^2-1 > 3 \]
Add 1 to both sides:
\[ (x-1)^2 > 4 \]
Take the square root of both sides, giving us two inequalities:
\[ x-1 > 2 \]
\[-(x-1) = 1-x > 2 \]
Rearrange these in terms of x:
\[ x > 3 \]
\[ x < -1 \]

Now put these on a number line :)