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3 Answers

Write the inequality as
x²-5x+15 < 0
 
Complete the square:
(x-2.5)²+8.75 < 0
 
The left-hand side is always positive, so the inequality has no solution (∅).
Adding to Andre's answer:
 
The polynomial x2 -5x +15 is a quadratic and represents a parabola that opens upward and vertex at (2.5, 8.75).  This parabola does cross the x axis, so at no point is y < 0

Comments

Your last sentence should be "The parabola doesn't cross the x-axis, etc"

Comment

Hi Leigh;
x²+15<5x
You are going to proceed as if the < is an = sign, with one exception.  If you multiply or divide both sides by a negative number, then < has to be reversed to >.
x²+15<5x
Let's subtract 5x from both sides...
x2-5x+15<5x-5x
x2-5x+15<0
We can go further, and subtract 15 from both sides...
x2-5x+15-15<0-15
x2-5x<-15
We can multiply both sides by -1...
-1(x2-5x)>-15(-1)
-x2+5x>15
We can factor...
-x(x-5)>15
or
x(-x+5)>15