x²+15<5x

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 (∅).

x²+15<5x

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New Wilmington, PA

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 (∅).

Olathe, KS

Adding to Andre's answer:

The polynomial x^{2} -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

Middletown, CT

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...

x^{2}-5x+15<5x-5x

x^{2}-5x+15<0

We can go further, and subtract 15 from both sides...

x^{2}-5x+15-15<0-15

x^{2}-5x<-15

We can multiply both sides by -1...

-1(x^{2}-5x)>-15(-1)

-x^{2}+5x>15

We can factor...

-x(x-5)>15

or

x(-x+5)>15

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