Given the inequality: x(−4+14)<0 To solve this inequality, we must first solve the corresponding equation: x(−4+14)=0 Solve: Given the linear equation:
(sqrt(14)-4)*x = 0
Expand brackets in the left part
sqrt+14-4)*x = 0
Move free summands (without x) from left part to right part, we given: x(−4+14)+4=4 Divide both parts of the equation by (4 + x*(-4 + sqrt(14)))/x
x = 4 / ((4 + x*(-4 + sqrt(14)))/x)
x1=0 x1=0 This roots x1=0 is the points with change the sign of the inequality expression. First define with the sign to the leftmost point: x0<x1 For example, let's take the point x0=x1−101 = −101 = −101 substitute to the expression x(−4+14)<0 10(−1)(−4+14)<0
____
2 \/ 14
- - ------ < 0
5 10
but
____
2 \/ 14
- - ------ > 0
5 10
Then x<0 no execute the solution of our inequality is: x>0