Question

Which inequality is the same as 7-2/b <5/b

Answer 1

Answer with explanation:

The given Inequality is:

`\rightarrow 7-(2)/(b)< (5)/(b)\\\\\rightarrow 7-(2)/(b)+(2)/(b)< (5)/(b)+(2)/(b)\\\\\rightarrow 7 < (7)/(b)\\\\\rightarrow b < (7)/(7)\\\\\rightarrow b<1`

→For, b=0 this inequality will be undefined.For , b <0 the inequality does not hold true because, for example,for b= -1, →7 <-7 is untrue, so for all negative value of b , the inequality does not hold true.

→The inequality which is same as inequality given is≡→0< b<1.

Answer 2

`\large\boxed{0<b<1}`

Explanation:

`Domain:\ b\\eq0\\\\7-(2)/(b)<(5)/(b)\qquad\text{add}\ (2)/(b)\ \text{to both sides}\\\\7<(7)/(b)\qquad\text{multiply both sides by}\ b\\\\1)\ \text{If}\ b<0\ \text{then we must flip the sign of inequality}\\\\7b>7\qquad\text{divide both sides by 7}\\\\b>1\to\text{contradiction, because is}\ b<0\\\\2)\ \text{If}\ b>0\ \text{then}\\\\7b<7\qquad\text{divide both sides by 7}\\\\b<1\ \text{and}\ b>0`