how to solve this

Question

x²+15<5x

Answer 1

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 (∅).

Answer 2

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

Answer 3

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