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 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 will first expand and simplify the equation.

1. Expand the right side: \[ 4x = 3x + 15 - 15 \] Simplifying this gives: \[ 4x = 3x \]

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

Now we analyze the solution:

• The simplified equation leads to \(x = 0\), which means there is one solution.

So the response is: The equation has one solution: \(x = 0\).