Undoing the operations gives \(\displaystyle x=\frac{29-b}{a}\). The largest numerator is \(28\), and the smallest divisor is \(2\), giving \(14\).

The smallest numerator is \(20\), and the largest divisor is \(4\), giving \(5\).

Both extreme combinations have integer solutions, and no other allowed numerator or divisor can exceed these bounds.

Answer

Largest: \(x=14\), from \(2x+1=29\). Smallest: \(x=5\), from \(4x+9=29\).