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

Question

4x = 3(x + 5) - 15
A. The equation has one solution: x = -10.
B. The equation has infinite solutions.
C. The equation has one solution: x = 0.
D. The equation has no solution.

Answer 1

To solve the equation \(4x = 3(x + 5) - 15\), we first simplify the right side:

1. Distribute the \(3\) on the right side: \[ 4x = 3x + 15 - 15 \]

2. Simplify \(15 - 15\): \[ 4x = 3x + 0 \] So, we have: \[ 4x = 3x \]

3. Next, subtract \(3x\) from both sides: \[ 4x - 3x = 0 \] Which simplifies to: \[ x = 0 \]

Now let's analyze the result:

• We found a single solution, \(x = 0\).

Therefore, the equation has one solution: C. The equation has one solution: x = 0.

Answer 2

are you sure this is correct

Answer 3

Yes, let's double-check the steps to ensure everything is clear and correct:

The original equation is:

\[ 4x = 3(x + 5) - 15 \]

1. Distributing the 3 on the right side:

   \[ 4x = 3x + 15 - 15 \]

2. Simplifying the right side:

   \[ 4x = 3x + 0 \] Which simplifies to: \[ 4x = 3x \]

3. Subtracting \(3x\) from both sides:

   \[ 4x - 3x = 0 \] This simplifies to: \[ x = 0 \]

This confirms that we indeed have one solution, which is \(x = 0\).

So the final answer is correct:

C. The equation has one solution: x = 0.