Solve for x

Question

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

The equation has no solution.

Answer 1

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

1. Expand the right side: \[ 4x = 3x + 15 - 15 \] This simplifies to: \[ 4x = 3x \]

2. Now, let's isolate \( x \) by subtracting \( 3x \) from both sides: \[ 4x - 3x = 0 \] Which simplifies to: \[ x = 0 \]

At this step, we find that there is one solution: \( x = 0 \).

Since we've found a specific value for \( x \), let's evaluate the nature of the solutions:

• The equation has one solution: \( x = 0 \).

Thus, the correct response is: The equation has one solution: x equals 0.