Solve for x

Question

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=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
.
The equation has one solution: x equals 3 .

The equation has no solution.

Answer 1

To solve the equation \( 9(x+1)=3(5x+1)−12 \), we will first simplify both sides.

Start by expanding both sides:

1. Left side: \[ 9(x+1) = 9x + 9 \]

2. Right side: \[ 3(5x + 1) - 12 = 15x + 3 - 12 = 15x - 9 \]

Now our equation looks like this: \[ 9x + 9 = 15x - 9 \]

Next, we will isolate \( x \) by moving \( 9x \) to the right side and moving \(-9\) to the left side: \[ 9 + 9 = 15x - 9x \] This simplifies to: \[ 18 = 6x \]

Now, divide both sides by 6: \[ x = 3 \]

Now let's determine the number of solutions: Since we found a specific value for \( x \), there is one solution.

Therefore, the final answer is: The equation has one solution: x = 3.