Question

Solve for x to determine if the equation has one, none, or infinite solutions.
9(x + 1) = 3(5x + 1) - 12
A. The equation has one solution: x = 3.
B. The equation has one solution: x = 0.
C. The equation has infinite solutions.
D. The equation has no solution.

Answer 1

Let's solve the equation step by step:

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

First, expand both sides:

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

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

Now we have the equation:
\[ 9x + 9 = 15x - 9 \]

Next, let's isolate \( x \) by first moving the terms involving \( x \) to one side and the constant terms to the other side.

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:
\[ x = 3 \]

Since we found one specific value for \( x \), the equation has one solution.

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