To determine how many solutions each equation has, we need to analyze the left and right sides.
1. **10x + 17 = 10x + 17**
- This simplifies to \(0 = 0\), which means both sides are always equal for any value of \(x\).
- **Infinite Solutions**
2. **10x + 17 = 10x + 18**
- This simplifies to \(0 = 1\), which is a contradiction.
- **Zero Solutions**
3. **17x + 18 = 17x + 18**
- This simplifies also to \(0 = 0\), which is true for any \(x\).
- **Infinite Solutions**
Now we can match them:
- **Zero Solutions:** 10x + 17 = 10x + 18
- **One Solution:** (No equation matches this category.)
- **Infinite Solutions:** 10x + 17 = 10x + 17 and 17x + 18 = 17x + 18
So the final match result is:
- Zero Solutions: **10x + 18**
- One Solution: **(none)**
- Infinite Solutions: **10x + 17** and **17x + 18**