Solve for x
to determine if the equation has one, none, or infinite solutions.
9(x+1)=3(5x+1)−12
(1 point)
Responses
The equation has one solution: x=3
.
The equation has one solution: x equals 3 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=0
.
The equation has one solution: x equals 20 .
The equation has infinite solutions.
The equation has infinite solutions.
9(x+1)=3(5x+1)-12
Distributing on both sides of the equation:
9x + 9 = 15x + 3 - 12
Combining like terms:
9x + 9 = 15x - 9
Subtracting 15x from both sides:
-6x + 9 = - 9
Subtracting 9 from both sides:
-6x = -18
Dividing both sides by -6:
x = 3
Therefore, the solution to the equation is x = 3. Therefore, the equation has one solution.
To solve for x in the equation 9(x+1)=3(5x+1)−12, we can start by simplifying both sides of the equation.
9(x+1) = 3(5x+1) - 12
Expanding the parentheses:
9x + 9 = 15x + 3 - 12
Combine like terms:
9x + 9 = 15x - 9
Now, let's isolate the variable x on one side of the equation. Subtract 9x from both sides:
9 = 6x - 9
Next, add 9 to both sides of the equation:
18 = 6x
Then, divide both sides by 6:
3 = x
Therefore, the solution to the equation is x = 3.