Solve the inequality State the solution using interval notat

Solve the inequality. State the solution using interval notation. You can solve this problem algebraically or geometrically. 65x < 28(1 + x2)

65x < 28 ( 1+ x^2 )

65x < 28 + 28x^2

subtracting 65x from both sides , the inequality becomes

28x^2 - 65x + 28 > 0

(7x-4)(4x-7) > 0

critical points are 4/7 , 7/4

--------------4/7 ------------- 7/4 -----------------

checking the inequality at 3 intervals ( -infinity , 4/7) , (4/7, 7/4) and ( 7/4 , infinity )

solution is

x < 4/7

x > 7/4

interval notation

( -infinity , 4/7) U ( 7/4 , infinity )