Answer
All real numbers are solutions.
Work Step by Step
The given inequality is
$\Rightarrow 2(k-5)\lt 2k+5$
Use distributive property.
$\Rightarrow 2k-10\lt 2k+5$
Add $10$ to each side.
$\Rightarrow 2k-10+10\lt 2k+5+10$
Simplify.
$\Rightarrow 2k\lt 2k+15$
Subtract $2k$ from each side.
$\Rightarrow 2k-2k\lt 2k+15-2k$
Simplify.
$\Rightarrow 0\lt 15$
The inequality is true.
Hence, all real numbers are solutions.
