1. Write down the equation: 10x - 7 = 8x + 9
2. Subtract 8x from both sides of the equation: 10x - 8x - 7 = 9
3. Simplify the expression: 2x - 7 = 9
4. Add 7 to both sides of the equation: 2x - 7 + 7 = 9 + 7
5. Simplify the expression: 2x = 16
6. Divide both sides by 2: x = \frac{16}{2}
7. Simplify to find the value of x: x = 8
The solution is x = 8.