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

Question

4x=3(x+5)−15 (1 point)
Responses

The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .

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

The equation has infinite solutions.
The equation has infinite solutions.

The equation has no solution

Answer 1

Let's start by solving the equation step by step:

Given the equation:

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

1. Distribute \(3\) on the right side:

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

2. Simplify the right side:

   \[ 4x = 3x \]

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

   \[ 4x - 3x = 0 \]

   \[ x = 0 \]

Now that we've solved for \(x\), we found that \(x = 0\).

Next, let's determine the type of solution.

Since we have found a specific value for \(x\) (which is \(0\)), the equation has one solution.

Thus, the answer is:

The equation has one solution: x=0.