Solve for x to determine if the equation has one, none, or infinite solutions.

Question

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.