To rewrite the equation \( a = 10b - 7 \) in terms of \( b \), Arthur should first isolate the term that contains \( b \). To do this, he should add 7 to both sides of the equation.
Here's how it looks:
Starting with: \[ a = 10b - 7 \]
Adding 7 to both sides: \[ a + 7 = 10b \]
So, the value he should add to both sides of the equation is 7.