Question

If $-\frac{5}{2}<-2m+1<-\frac{7}{5}$, find the maximum value (in integer) of the expression $10m-5$.

• A. $6$
• B. $7$
• C. $10$
• D. $12$

Answer 1

The correct option is D $12$

$-\frac{5}{2}<-2m+1<-\frac{7}{5}$

Divided all sides with $-5$. we get

$-\frac{5}{2}\times (-5)\ge -5(-2m+1)\ge -\frac{7}{5}\times (-5)$

$\Rightarrow \frac{25}{2}\ge 10m-5\ge 7$

$\Rightarrow 12.5\ge 10m-5\ge 7$

As per above, the value of $10m-5$ is less than $12.5$, then the maximum value (in integer) of $2m-5$ is $12$. ( Because the replacement set is $Z$)