1. Let x be the smallest integer,
Set up the expression for the problem: 5x \geq 3(x+1) + 8
2. Distribute and simplify: 5x \geq 3x + 3 + 8
3. Combine like terms: 5x \geq 3x + 11
4. Isolate the variable: 2x \geq 11
5. Solve for the smallest integer: x \geq 5.5 , so the smallest integer is 6.
6. The integers are 6 and 7.
7. Answer: (6, 7)