To determine if the equation \(9(x + 1) = 3(5x + 1) - 12\) has one, none, or infinite solutions, let's start by simplifying both sides of the equation step by step:
- Expand both sides.
The left side: \[ 9(x + 1) = 9x + 9 \]
The right side: \[ 3(5x + 1) - 12 = 15x + 3 - 12 = 15x - 9 \]
Now we can rewrite the equation: \[ 9x + 9 = 15x - 9 \]
- Next, we will rearrange the equation to isolate \(x\).
Subtract \(9x\) from both sides: \[ 9 = 15x - 9x - 9 \] \[ 9 = 6x - 9 \]
Now add \(9\) to both sides: \[ 9 + 9 = 6x \] \[ 18 = 6x \]
- Finally, divide both sides by \(6\): \[ x = 3 \]
The solution is \(x = 3\).
Now, we can conclude that the equation has one solution: \(x = 3\).
So, the correct response is: The equation has one solution: x = 3.
3 answers