Question

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

The equation has no solution.
The equation has no solution.

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=0
.

Answer 1

Let's solve the equation step by step:

Given:
\[ 9(x + 1) = 3(5x + 1) - 12 \]

First, simplify both sides:

1. Expand the left side:
\[ 9(x + 1) = 9x + 9 \]

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

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

Next, we want to get all the terms involving \(x\) on one side and the constant terms on the other. To do that, we subtract \(9x\) from both sides:
\[ 9 = 15x - 9x - 9 \]
\[ 9 = 6x - 9 \]

Now add \(9\) to both sides:
\[ 9 + 9 = 6x \]
\[ 18 = 6x \]

Now divide both sides by \(6\):
\[ x = \frac{18}{6} \]
\[ x = 3 \]

Now that we have our solution, let's determine how many solutions we have. Since we derived a single value for \(x\), we conclude that the equation has **one solution: x = 3**.

So, the correct response is:
**The equation has one solution: x = 3.**