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=0

B). The equation has infinite solutions.

C). The equation has no solution.

D). The equation has one solution: x=3

Answer 1

To solve the equation \( 9 (x + 1) = 3 (5x + 1) - 12 \), we will simplify both sides step by step.

1. Expand both sides:

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

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

2. Now, we rewrite the equation with the simplified sides: \[ 9x + 9 = 15x - 9 \]

3. Next, let's isolate \(x\) by moving all terms involving \(x\) to one side and constant terms to the other side: \[ 9 + 9 = 15x - 9x \] Simplifying this gives: \[ 18 = 6x \]

4. Divide both sides by 6 to solve for \(x\): \[ x = 3 \]

Since we found a single solution \(x = 3\), the conclusion is that the equation has one solution.

The correct answer is:

D). The equation has one solution: x = 3.