Whereas the direction is reversed if each side is multiplied by a negative real number?
Answer to Problem 131AYU
Explanation of Solution
Given information:
How would you explain to a fellow student the underlying reason for the multiplication properties for inequalities that is , the sense or direction of an inequality remains the same if each side is multiplied by a positive real number, whereas the direction is reversed if each side is multiplied by a negative real number?
Calculation:
We have to prove that the sense or direction of an inequality remain the same if each side is multiplied by a positive real number, whereas the direction is reversed if each side is multiplied by a negative number. That is:
If
If
For: if
From
and
We know that the product of two positive quantities is again a positive quantity. Hence, multiplying (1) and (2) we have:
Thus if
For: if
Also
We know that the product of a positive quantity and a negative quantity is a negative quantity.
Hence, multiplying (1) and (3) we have:
Hence, if
Chapter A Solutions
Precalculus
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