# Solving Inequality with more than one parameter

I want to solve this inequality for x1 when a,b,d, E, and alpha
are positive parameters
I tried this code and I did not get the required answer

Reduce[{((a*alpha*x1)/(b + x1) - d*alpha)*((a*alpha*x1)/(b + x1) - (d+E)*alpha) <= 0,x1 > 0}, x1]

I will appreciate any help

• E is a reserved symbol in Mathematica.
– Syed
Oct 2 at 8:59
• Reduce[{((a*\[Alpha]*x1)/(b + x1) - d*\[Alpha])*((a*\[Alpha]*x1)/(b + x1) - (d + e)*\[Alpha]) <= 0, x1 > 0}, x1, PositiveReals] ?
– Syed
Oct 2 at 9:03
• May I suggest a more manual approach? Your inequality has the form P*Q <= 0. This means that either P>=0 and Q<=0, or alternatively, P<=0 and Q>=0. You will probably get a better understanding if you first run Solve[P==0,x1] and Solve[Q==0,x1], this will tell you for which values x1 the factors P and Q change signs. Oct 2 at 9:12
• thanks a lot for your help. I will try this approach Oct 3 at 7:09

First, as already mention replace E by e. Then define {a,b,d,e,x1}>0. With these changes you will get an answer:

 Reduce[{((a*alpha*x1)/(b + x1) -
d*alpha)*((a*alpha*x1)/(b + x1) - (d + e)*alpha) <=
0, {a, b, d, e, x1} > 0}, x1]


• thanks a lot for your help. I need to know what is the meaning of this || Oct 3 at 7:08
• The name for || is Or. It means different possibilities. On the other hand, && is And and means conditions that must be fulfilled simultaneously. Oct 3 at 7:37
• thank you so much Oct 3 at 10:14

A more general answer is obtained in 13.1 on Windows 10 as follows.

Reduce[{((a*α*x1)/(b + x1) -  d*α)*((a*α*x1)/(b + x1)
- (d + e)*α) <= 0,  x1 > 0}, x1, Reals]

*(e < 0 && ((d <
0 && ((a <
d + e && ((α < 0 &&
b > 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b > 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)))) || (a ==
d + e && ((α <
0 && ((b == 0 && x1 > 0) || (b > 0 &&
x1 >= -((b d)/(-a + d))))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b == 0 && x1 > 0) || (b > 0 &&
x1 >= -((b d)/(-a + d))))))) || (d + e < a <
d && ((α <
0 && ((b < 0 &&
x1 >= (-b d - b e)/(-a + d + e)) || (b == 0 &&
x1 > 0) || (b > 0 &&
x1 >= -((b d)/(-a + d))))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
x1 >= (-b d - b e)/(-a + d + e)) || (b == 0 &&
x1 > 0) || (b > 0 &&
x1 >= -((b d)/(-a + d))))))) || (a ==
d && ((α <
0 && ((b < 0 &&
x1 >= (-b d - b e)/(-a + d + e)) || (b == 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
x1 >= (-b d - b e)/(-a + d + e)) || (b == 0 &&
x1 > 0))))) || (d < a <
0 && ((α < 0 &&
b < 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b < 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))))) || (a == 0 && α ==
0 && ((b <=
0 && (0 < x1 < (-b d - b e)/(d + e) ||
x1 > (-b d - b e)/(d + e))) || (b > 0 &&
x1 > 0))) || (a >
0 && ((α < 0 &&
b < 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b < 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)))))) || (d ==
0 && ((a <
e && ((α < 0 && b > 0 &&
0 < x1 <= -((b e)/(-a + e))) || (α ==

0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b > 0 &&
0 < x1 <= -((b e)/(-a + e))))) || (a ==
e && ((α < 0 && b >= 0 &&
x1 > 0) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b >= 0 &&
x1 > 0))) || (e < a <
0 && ((α <
0 && ((b < 0 && x1 >= -((b e)/(-a + e))) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 && x1 >= -((b e)/(-a + e))) || (b >= 0 &&
x1 > 0))))) || (a ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (a >
0 && ((α < 0 && b < 0 &&
0 < x1 <= -((b e)/(-a + e))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b < 0 &&
0 < x1 <= -((b e)/(-a + e))))))) || (0 <
d < -e && ((a <
d + e && ((α <
0 && ((b < 0 &&
0 < x1 <= -((b d)/(-a + d))) || (b > 0 &&
0 < x1 <= (-b d - b e)/(-a + d +
e)))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
0 < x1 <= -((b d)/(-a + d))) || (b > 0 &&
0 < x1 <= (-b d - b e)/(-a + d + e)))))) || (a ==
d + e && ((α <
0 && ((b < 0 &&
0 < x1 <= -((b d)/(-a + d))) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
0 < x1 <= -((b d)/(-a + d))) || (b >= 0 &&
x1 > 0))))) || (d + e < a <
0 && ((α <
0 && ((b <
0 && (0 < x1 <= -((b d)/(-a + d)) ||
x1 >= (-b d - b e)/(-a + d + e))) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b <
0 && (0 < x1 <= -((b d)/(-a + d)) ||
x1 >= (-b d - b e)/(-a + d + e))) || (b >= 0 &&
x1 > 0))))) || (a ==
0 && ((b <=
0 && (0 < x1 < (-b d - b e)/(d + e) ||
x1 > (-b d - b e)/(d + e))) || (b > 0 &&
x1 > 0))) || (0 < a <
d && ((α <
0 && ((b <
0 && (0 < x1 <= (-b d - b e)/(-a + d + e) ||
x1 >= -((b d)/(-a + d)))) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b <
0 && (0 < x1 <= (-b d - b e)/(-a + d + e) ||
x1 >= -((b d)/(-a + d)))) || (b >= 0 &&
x1 > 0))))) || (a ==
d && ((α <
0 && ((b < 0 &&
0 < x1 <= (-b d - b e)/(-a + d + e)) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
0 < x1 <= (-b d - b e)/(-a + d + e)) || (b >= 0 &&
x1 > 0))))) || (a >
d && ((α <
0 && ((b < 0 &&
0 < x1 <= (-b d - b e)/(-a + d + e)) || (b > 0 &&
0 < x1 <= -((b d)/(-a + d))))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
0 < x1 <= (-b d - b e)/(-a + d + e)) || (b > 0 &&
0 < x1 <= -((
b d)/(-a + d))))))))) || (d == -e && ((a <
0 && ((α < 0 && b < 0 &&
0 < x1 <= -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b < 0 &&
0 < x1 <= -((b d)/(-a + d))))) || (a ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (0 < a <
d && ((α <
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b >= 0 &&
x1 > 0))))) || (a ==
d && ((α < 0 && b >= 0 &&
x1 > 0) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b >= 0 &&
x1 > 0))) || (a >
d && ((α < 0 && b > 0 &&
0 < x1 <= -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b > 0 &&
0 < x1 <= -((b d)/(-a + d))))))) || (d > -e && ((a <

0 && ((α < 0 &&
b < 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b < 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))))) || (a == 0 && α ==
0 && ((b <=
0 && (0 < x1 < (-b d - b e)/(d + e) ||
x1 > (-b d - b e)/(d + e))) || (b > 0 &&
x1 > 0))) || (0 < a <
d + e && ((α < 0 &&
b < 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b < 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)))) || (a ==
d + e && ((α <
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b == 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b == 0 &&
x1 > 0))))) || (d + e < a <
d && ((α <
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b == 0 &&
x1 > 0) || (b > 0 &&
x1 >= (-b d - b e)/(-a + d + e)))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b == 0 &&
x1 > 0) || (b > 0 &&
x1 >= (-b d - b e)/(-a + d + e)))))) || (a ==
d && ((α <
0 && ((b == 0 && x1 > 0) || (b > 0 &&
x1 >= (-b d - b e)/(-a + d + e)))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b == 0 && x1 > 0) || (b > 0 &&
x1 >= (-b d - b e)/(-a + d + e)))))) || (a >
d && ((α < 0 &&
b > 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b > 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))))))))) || (e ==
0 && ((d <
0 && ((a <
d && ((α < 0 && b > 0 &&
x1 == -((b d)/(-a + d))) || (α ==

0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b > 0 &&
x1 == -((b d)/(-a + d))))) || (a ==
d && ((α < 0 && b == 0 &&
x1 > 0) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b == 0 &&
x1 > 0))) || (d < a <
0 && ((α < 0 && b < 0 &&
x1 == -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b < 0 &&
x1 == -((b d)/(-a + d))))) || (a == 0 && α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (a >
0 && ((α < 0 && b < 0 &&
x1 == -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b < 0 &&
x1 == -((b d)/(-a + d))))))) || (d ==
0 && ((a < 0 && α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (a ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (a > 0 && α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))))) || (d >
0 && ((a <
0 && ((α < 0 && b < 0 &&
x1 == -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b < 0 &&
x1 == -((b d)/(-a + d))))) || (a == 0 && α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (0 < a <
d && ((α < 0 && b < 0 &&
x1 == -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b < 0 &&
x1 == -((b d)/(-a + d))))) || (a ==
d && ((α < 0 && b == 0 &&
x1 > 0) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b == 0 &&
x1 > 0))) || (a >
d && ((α < 0 && b > 0 &&
x1 == -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b > 0 &&
x1 == -((b d)/(-a + d))))))))) || (e >
0 && ((d < -e && ((a <
d && ((α < 0 &&
b > 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b > 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))))) || (a ==
d && ((α <
0 && ((b == 0 && x1 > 0) || (b > 0 &&
x1 >= (-b d - b e)/(-a + d + e)))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b == 0 && x1 > 0) || (b > 0 &&
x1 >= (-b d - b e)/(-a + d + e)))))) || (d < a <
d + e && ((α <
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b == 0 &&
x1 > 0) || (b > 0 &&
x1 >= (-b d - b e)/(-a + d + e)))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b == 0 &&
x1 > 0) || (b > 0 &&
x1 >= (-b d - b e)/(-a + d + e)))))) || (a ==
d + e && ((α <
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b == 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b == 0 &&
x1 > 0))))) || (d + e < a <
0 && ((α < 0 &&
b < 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b < 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)))) || (a ==
0 && α ==
0 && ((b <=
0 && (0 < x1 < (-b d - b e)/(d + e) ||
x1 > (-b d - b e)/(d + e))) || (b > 0 &&
x1 > 0))) || (a >
0 && ((α < 0 &&
b < 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b < 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))))))) || (d == -e && ((a <

d && ((α < 0 && b > 0 &&
0 < x1 <= -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b > 0 &&
0 < x1 <= -((b d)/(-a + d))))) || (a ==
d && ((α < 0 && b >= 0 &&
x1 > 0) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b >= 0 &&
x1 > 0))) || (d < a <
0 && ((α <
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 && x1 >= -((b d)/(-a + d))) || (b >= 0 &&
x1 > 0))))) || (a ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (a >
0 && ((α < 0 && b < 0 &&
0 < x1 <= -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b < 0 &&
0 < x1 <= -((b d)/(-a + d))))))) || (-e < d <
0 && ((a <
d && ((α <
0 && ((b < 0 &&
0 < x1 <= (-b d - b e)/(-a + d + e)) || (b > 0 &&
0 < x1 <= -((b d)/(-a + d))))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
0 < x1 <= (-b d - b e)/(-a + d + e)) || (b > 0 &&
0 < x1 <= -((b d)/(-a + d))))))) || (a ==
d && ((α <
0 && ((b < 0 &&
0 < x1 <= (-b d - b e)/(-a + d + e)) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
0 < x1 <= (-b d - b e)/(-a + d + e)) || (b >= 0 &&
x1 > 0))))) || (d < a <
0 && ((α <
0 && ((b <
0 && (0 < x1 <= (-b d - b e)/(-a + d + e) ||
x1 >= -((b d)/(-a + d)))) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b <
0 && (0 < x1 <= (-b d - b e)/(-a + d + e) ||
x1 >= -((b d)/(-a + d)))) || (b >= 0 &&
x1 > 0))))) || (a ==

0 && ((b <=
0 && (0 < x1 < (-b d - b e)/(d + e) ||
x1 > (-b d - b e)/(d + e))) || (b > 0 &&
x1 > 0))) || (0 < a <
d + e && ((α <
0 && ((b <
0 && (0 < x1 <= -((b d)/(-a + d)) ||
x1 >= (-b d - b e)/(-a + d + e))) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b <
0 && (0 < x1 <= -((b d)/(-a + d)) ||
x1 >= (-b d - b e)/(-a + d + e))) || (b >= 0 &&
x1 > 0))))) || (a ==
d + e && ((α <
0 && ((b < 0 &&
0 < x1 <= -((b d)/(-a + d))) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
0 < x1 <= -((b d)/(-a + d))) || (b >= 0 &&
x1 > 0))))) || (a >
d + e && ((α <
0 && ((b < 0 &&
0 < x1 <= -((b d)/(-a + d))) || (b > 0 &&
0 < x1 <= (-b d - b e)/(-a + d +
e)))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
0 < x1 <= -((b d)/(-a + d))) || (b > 0 &&
0 < x1 <= (-b d - b e)/(-a + d + e)))))))) || (d ==
0 && ((a <
0 && ((α < 0 && b < 0 &&
0 < x1 <= -((b e)/(-a + e))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b < 0 &&
0 < x1 <= -((b e)/(-a + e))))) || (a ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (0 < a <
e && ((α <
0 && ((b < 0 && x1 >= -((b e)/(-a + e))) || (b >= 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 && x1 >= -((b e)/(-a + e))) || (b >= 0 &&
x1 > 0))))) || (a ==
e && ((α < 0 && b >= 0 &&
x1 > 0) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b >= 0 &&
x1 > 0))) || (a >
e && ((α < 0 && b > 0 &&
0 < x1 <= -((b e)/(-a + e))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 && b > 0 &&
0 < x1 <= -((b e)/(-a + e))))))) || (d >
0 && ((a <
0 && ((α < 0 &&
b < 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b < 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)))) || (a ==
0 && α ==
0 && ((b <=
0 && (0 < x1 < (-b d - b e)/(d + e) ||
x1 > (-b d - b e)/(d + e))) || (b > 0 &&
x1 > 0))) || (0 < a <
d && ((α < 0 &&
b < 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b < 0 && (-b d - b e)/(-a + d + e) <=
x1 <= -((b d)/(-a + d))))) || (a ==
d && ((α <
0 && ((b < 0 &&
x1 >= (-b d - b e)/(-a + d + e)) || (b == 0 &&
x1 > 0))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
x1 >= (-b d - b e)/(-a + d + e)) || (b == 0 &&
x1 > 0))))) || (d < a <
d + e && ((α <
0 && ((b < 0 &&
x1 >= (-b d - b e)/(-a + d + e)) || (b == 0 &&
x1 > 0) || (b > 0 &&
x1 >= -((b d)/(-a + d))))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b < 0 &&
x1 >= (-b d - b e)/(-a + d + e)) || (b == 0 &&
x1 > 0) || (b > 0 &&
x1 >= -((b d)/(-a + d))))))) || (a ==
d + e && ((α <
0 && ((b == 0 && x1 > 0) || (b > 0 &&
x1 >= -((b d)/(-a + d))))) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α >
0 && ((b == 0 && x1 > 0) || (b > 0 &&
x1 >= -((b d)/(-a + d))))))) || (a >
d + e && ((α < 0 &&
b > 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e)) || (α ==
0 && ((b <= 0 && (0 < x1 < -b || x1 > -b)) || (b > 0 &&
x1 > 0))) || (α > 0 &&
b > 0 && -((b d)/(-a + d)) <=
x1 <= (-b d - b e)/(-a + d + e))))))))*

• thanks a lot for your help . Oct 3 at 7:08