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