Question

7) If a> b and m<0, then which of the following is
correct?
i. am<bm
ii. am=bm
iii. am>bm
iv. am and bm cannot be compared.​

Answer 1

Answer:

option 3........................

Answer 2

Answer:

The correct option for the given problem is found to be option (i) am < bm.

Step-by-step explanation:

We know that for any pair of real numbers, a and b, such that, a > b, the sign of inequality is reversed if the negative sign is introduced at both sides of the sign of inequality, i.e., the relation now becomes -ak < -bk or -a < -b, where 'k' is any real constant.

Here we are given that a > b as well as m < 0, which means that 'm' is a negative real number.

Let $m = -n$, where 'n' is a real number.

Now, $a > b$          (given)

As discussed above, Multiplying both sides of the inequality by -n, we get:

$-an < -bn$

but we know that $m = -n$, so:

$am < bm$

Thus, option (i) is the correct answer.