+0  
 
0
34
3
avatar

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

 

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

 Feb 18, 2021
 #1
avatar
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).

 Feb 18, 2021
 #2
avatar+29088 
+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 , +∞)

 Feb 18, 2021
 #3
avatar+29088 
+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, +∞)   

 Feb 18, 2021

74 Online Users

avatar
avatar
avatar
avatar
avatar