To rewrite the equation \( a = 10b - 7 \) in terms of \( b \), the first step is to isolate the term containing \( b \).
To do this, we can add \( 7 \) to both sides of the equation. This gives us:
\[ a + 7 = 10b \]
So, the value Arthur should add to both sides of the equation is \( 7 \).