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

The equation has infinite solutions.

Answer 1

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

### Step 1: Distribute the terms on both sides

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

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

### Step 2: Set the equation up

Now we can rewrite the original equation with the simplified terms:
\[
9x + 9 = 15x - 9
\]

### Step 3: Rearranging the equation

To solve for \(x\), we'll move the terms involving \(x\) to one side and the constant terms to the other side:
\[
9 + 9 = 15x - 9x
\]
\[
18 = 6x
\]

### Step 4: Solve for \(x\)

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

### Conclusion:

We found that \(x = 3\).

Therefore, the equation has one solution: \(x = 3\).