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 infinite solutions.
The equation has infinite solutions.

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.

Answer 1

To solve the equation \(4x = 3(x + 5) - 15\), we'll first simplify and solve for \(x\).

1. Distribute on the right side:
\[
3(x + 5) = 3x + 15
\]
So, the equation becomes:
\[
4x = 3x + 15 - 15
\]
Simplifying the right side:
\[
4x = 3x + 0
\]
Which simplifies to:
\[
4x = 3x
\]

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

Now, we found one solution: \(x = 0\).

Next, we check if the equation has infinite solutions or no solutions. Since we reached a consistent solution, we conclude that the equation has one solution.

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