Is there any general rule for multiplication or division of two inequalities?
a<x<b and c<y<d
Now is there any rule to find the relationships for xy or x/y?
Thank you in advance!
Multiplication - Yes but very constrained.
If both sides of both inequalities are positive and the inequalities have the same sign, you can multiply them.
x < a
y < b
xy < ab
Given x, y, a, b are all positive.
-2 < -1
10 < 30
Multiply: -20 < -30 (Not correct)
-2 < 7
-8 < 1
Multiply: 16 < 7 (Not correct)
For division, this may not hold.
2 < 10
4 < 40
Divide: 1/2 < 1/4
But if both sides of both the inequalities are positive and the signs of the inequality are opposite, then you can divide them
x < a
y > b
x/y < a/b (given all x, y, a, b are positive)
The final inequality takes the sign of the numerator. Take examples.
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