1. Solve the inequality \(x(x + 6) > 16.\)

2. Solve the inequality \(x^3 + 4x > 5x^2.\)

Guest Feb 18, 2021

#1**0 **

1. The roots are -8 and 2, so the solution is (-8,2).

2. First, we can divide both sides by x to get x^2 + 4 > 5x, so x^2 - 5x + 4 > 0. The roots are 1 and 4, so the solution is (1,4).

Guest Feb 18, 2021

#2**+1 **

x(x+6) - 16 >0

x^2 +6x -16 > 0

(x+8)(x-2) > 0

roots are -8 and +2

this is a bowl shaped parabola .....between -8 an +2 it is below zero (or = to zero) ....above zero elsewhere

(-∞, -8)** U** ( 2 , +∞)

ElectricPavlov Feb 18, 2021

#3**+1 **

x (x^2 -5x+4) >0

x (x-4)(x-1 ) >0

roots 0 4 1 we have to determine what the value is between these roots to see if >0

From 0 -1 it is positive (but = 0 at 0 and 1, so those points are not included) and from > 4 to infinity it is positive

it is <0 elsewhere

(0,1)** U** (4, +∞)

ElectricPavlov Feb 18, 2021