Solve for x to determine if the equation has one, none or infinite solutions.

9 (x+1)=3 (5x+1)-12

To solve for x, let's simplify the equation step by step:

Start with 9(x + 1) = 3(5x + 1) - 12.

Expanding both sides of the equation:
9x + 9 = 15x + 3 - 12.

Combine like terms:
9x + 9 = 15x - 9.

Subtract 9x from both sides:
9 = 6x - 9.

Add 9 to both sides:
18 = 6x.

Divide both sides by 6:
x = 3.

Therefore, the equation has one solution: x = 3.

Let's simplify the equation step by step:

Starting with the left side of the equation:
9(x + 1)

Distribute the 9:
9x + 9

Now, moving on to the right side of the equation:
3(5x + 1) - 12

Distribute the 3:
15x + 3 - 12

Combine like terms:
15x - 9

Now, we have:
9x + 9 = 15x - 9

Let's isolate the x terms by subtracting 9x from both sides:
9 = 6x - 9

Next, let's isolate the constant terms by adding 9 to both sides:
18 = 6x

Finally, divide both sides by 6 to solve for x:
x = 3

Therefore, the equation has one solution, which is x = 3.