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 no solution.
The equation has no solution.

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 one solution: x=−10.

Answer 1

To solve the equation \( 4x = 3(x + 5) - 15 \), we will start by simplifying the right side.

1. Expand the right side:
\[
3(x + 5) = 3x + 15
\]
So,
\[
3(x + 5) - 15 = 3x + 15 - 15 = 3x
\]

2. Now, we have the equation:
\[
4x = 3x
\]

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

Now we check the conclusions:
- The equation \( 4x = 3(x + 5) - 15 \) simplifies to \( 4x = 3x \), which leads us to \( x = 0 \).
- This means there is one solution.

Thus, the answer is:
**The equation has one solution: x=0.**