Solve for x to determine if the equation has one, none, or infinite solutions.9(x+1)=3(5x+1)−12 (1 point)ResponsesThe 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.

Answer 1

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

Starting from the left side: \[ 9(x + 1) = 9x + 9 \]

Now simplifying the right side: \[ 3(5x + 1) - 12 = 15x + 3 - 12 = 15x - 9 \]

Now we equate both sides: \[ 9x + 9 = 15x - 9 \]

Next, we will move all terms involving \( x \) to one side and constant terms to the other side: \[ 9 + 9 = 15x - 9x \] \[ 18 = 6x \]

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

We have found one solution: \( x = 3 \).

Now, we check to see if there are any restrictions or other solutions. In this case, since we derived a unique solution from the simplification and did not end up with a contradictory statement (like \( 0 = 5 \)), we can conclude:

The equation has one solution: \( x = 3 \).