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

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

Answer 1

To solve this equation, let's simplify both sides of the equation:

4x = 3(x+5) - 15

First, distribute the 3 to both terms inside the parentheses:

4x = 3x + 15 - 15

Combine like terms:

4x = 3x

Since the 3x terms are the same on both sides of the equation, we can subtract 3x from both sides to isolate the variable:

4x - 3x = 3x - 3x

Simplifying further:

x = 0

Therefore, the equation has one solution: x = 0.