Answer:
No solution:
![3x+9+4x+x=8x+1](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5ijern7ube89wdwv8spvq8durg9mu71z0m.png)
One solution:
![3x+9+4x+x=2x+3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5o9edra84lo1ilys1n7eu04lfximk9jvj6.png)
Infinitely many solution:
![3x+9+4x+x=8x+9](https://img.qammunity.org/2020/formulas/mathematics/middle-school/m0rmfoohkiv7owh3smwxfhkb7l3mk7m5tb.png)
Explanation:
The given equation is
![3x+9+4x+x=___](https://img.qammunity.org/2020/formulas/mathematics/middle-school/680gfuqu0tps13y66rtbr8h2c0yioucih4.png)
It can be written as
![8x+9=___](https://img.qammunity.org/2020/formulas/mathematics/middle-school/uol6ocjxf0spz3cetr1ha6tddxcimjsis5.png)
Here slope is 8 and y-intercept is 9.
No solution: For all values of x, LHS≠RHS. It means the lines have same slope but different y-intercept.
![3x+9+4x+x=8x+1](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5ijern7ube89wdwv8spvq8durg9mu71z0m.png)
One solution: For unique value of x, LHS=RHS. It means the lines have different slopes.
![3x+9+4x+x=2x+3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5o9edra84lo1ilys1n7eu04lfximk9jvj6.png)
Infinitely many solution: For all values of x, LHS=RHS. It means the lines have same slope and y-intercept.
![3x+9+4x+x=8x+9](https://img.qammunity.org/2020/formulas/mathematics/middle-school/m0rmfoohkiv7owh3smwxfhkb7l3mk7m5tb.png)
Note: There are more possible equations for no solutions and one solution.