For given operators $a$ and $b$, find all operators satisfying in $\|a-bx\|\leq 1$.

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Let $H$ be a Hilbert space and consider operators $a$ and $b$ on $H$. I am looking forward to any approach that leads me to formulate operators $ x$, in terms of $a$ and $b$, satisfying in the inequality $\|a-bx\|\leq1$.