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 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.
The equation has one solution: x=3
.
Simplifying both sides of the equation:
9(x+1) = 3(5x+1) - 12
9x + 9 = 15x + 3 - 12
9x + 9 = 15x - 9
Subtracting 9x from both sides:
9 = 6x - 9
Adding 9 to both sides:
18 = 6x
Dividing by 6:
3 = x
Therefore, the equation has one solution: x = 3.
To solve the equation 9(x+1) = 3(5x+1) - 12, follow these steps:
Step 1: Distribute on both sides of the equation to eliminate parentheses:
9x + 9 = 15x + 3 - 12
Simplifying further:
9x + 9 = 15x - 9
Step 2: Group like terms on one side of the equation:
9x - 15x = -9 - 9
Simplifying further:
-6x = -18
Step 3: Divide both sides of the equation by -6 to solve for x:
x = -18 / -6
Simplifying further:
x = 3
Therefore, the equation has one solution: x = 3.