Answer:
No solutions: 8x + 11
One solution: 7x + 11
Infinitely many solutions: 8x + 9
Step-by-step explanation:
You know that 3x + 9 + 4x + x would naturally result to 8x + 9.
An equation with no solutions would consist of a solution that does not equal to the equation. If you put 3x + 9 + 4x + x = 8x + 11, this would result in the assumption that 8x + 9 = 8x + 11
8x + 9 = 8x + 11
9 ≠ 11
Since 9 does not equal to 11, 8x + 11 poses no solution to the value of x.
If you put 7x + 11 as the solution, you are suggesting that 8x + 9 = 7x + 11.
8x + 9 = 7x + 11
8x - 7x = 11 - 9
x = 2
In this case, you can see that x has a definite and only one value, so there is only one solution.
If you put 8x + 9 as the solution, you are suggesting that 8x + 9 = 8x + 9.
8x + 9 = 8x + 9
9 = 9
In this case, you realise that any number can take the value of x and still satisfy as a solution, so it has infinitely many solutions.
