1. Solve the inequality \(x(x + 6) > 16.\)
2. Solve the inequality \(x^3 + 4x > 5x^2.\)
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).
+37157 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 , +∞)
+37157 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, +∞)
