Question

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
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
x
=
3
.

Answer 1

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:

1. 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:
\[
9x + 9 = 15x - 9
\]

2. 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:
\[
9 + 9 = 6x
\]
\[
18 = 6x
\]

3. 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.**