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=−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 no solution.
The equation has no solution.

Answer 1

Let's solve the equation \(4x = 3(x + 5) - 15\) step by step.

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

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

Since we found a single solution, we can conclude that:

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