Answer
$1\lt k \lt 6$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow -3\lt 2k-5 \lt 7$
Add $5$ to each expression.
$\Rightarrow -3+5\lt 2k-5+5 \lt 7+5$
Simplify.
$\Rightarrow 2\lt 2k \lt 12$
Divide each expression by $2$.
$\Rightarrow \frac{2}{2}\lt \frac{2k}{2} \lt \frac{12}{2}$
Simplify.
$\Rightarrow 1\lt k \lt 6$
Hence, the solution is $1\lt k \lt 6$.
