Question

If $-3$ and $|5-4p|$ have the same absolute value and the sum of all possible values of $p$ is $k$, then the value of $2k$ is

Answer 1

Given, $|5-4p|=|-3|$
Now, $|5-4p|=3$
$\Rightarrow 5-4p=\pm 3\Rightarrow -4p=-5+3,-5-3\Rightarrow -4p=-2,-8\Rightarrow p=\frac{1}{2},2$
Sum of all values of $p=\frac{1}{2}+2=\frac{5}{2}$
$\Rightarrow k=\frac{5}{2}\therefore 2k=5$