if a<b, show that a<((mb+na)/(m+n))<b a,b,m,n are arbitrary constants


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Question Number 170838 by pablo1234523 last updated on 01/Jun/22

$if a < b, show that a < \frac{m b + n a}{m + n} < b$ $a, b, m, n are arbitrary constants$
	Answered by chengulapetrom last updated on 04/Jun/22

	$if a < b, show that a < \frac{m b + n a}{m + n} < b$ $a, b, m, n are arbitrary constants$ $n a < n b$ $m a < m b$ $n a + m a < m b + n a$ $a (m + n) < m b + n a$ $a < \frac{m b + n a}{m + n} . . . . . . . . . . . . . (i)$ $n a + m b < n b + m b$ $m b + n a < b (m + n)$ $\frac{m b + n a}{m + n} < b . . . . . . . . . . . . . . . (i i)$ $c o m b i n i n g (i) a n d (i i) y i e l d s$ $a < \frac{m b + n a}{m + n} < b$
	Commented bypablo1234523 last updated on 07/Jun/22

	$thanks sir .$ $but if n < 0 then n a > n b$ $then it will be incorrect$
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