Question

Question
Solve for x
to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15
(1 point)
Responses

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

The equation has no solution.
The equation has no solution.

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

The equation has infinite solutions.

Answer 1

To solve the equation \( 4x = 3(x + 5) - 15 \), let's simplify both sides step by step.

1. Start with the original equation:
\[
4x = 3(x + 5) - 15
\]

2. Distribute on the right side:
\[
4x = 3x + 15 - 15
\]
Simplifying the right side gives:
\[
4x = 3x + 0
\]
Which simplifies to:
\[
4x = 3x
\]

3. Subtract \( 3x \) from both sides:
\[
4x - 3x = 0
\]
This simplifies to:
\[
x = 0
\]

Now let's analyze the solutions:
- The equation has one unique solution: \( x = 0 \).

Thus, the correct response is:
**The equation has one solution: \( x = 0 \).**