To rewrite the equation \( a = 10b - 7 \) in terms of \( b \), Arthur needs to isolate \( b \).
In his first step, he should add \( 7 \) to both sides of the equation. This gives:
\[ a + 7 = 10b \]
This step allows him to eliminate the \( -7 \) from the right side, making it easier to isolate \( b \) in subsequent steps.