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=−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.

Answer 1

To solve the equation \( 4x = 3(x + 5) - 15 \), we will first simplify the right side of the equation:

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

2. Now, we can isolate \( x \) by subtracting \( 3x \) from both sides: \[ 4x - 3x = 0 \] \[ x = 0 \]

We have found one solution, \( x = 0 \).

Now, let’s determine the number of solutions:

• We arrived at the equation \( x = 0 \), which indicates that there is one unique solution.

Thus, the equation has one solution: \( x = 0 \).