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.