Solve for x to determine if the equation has one, none, or infinite solutions.

Question

3(x+2)−6=3x (1 point)
Responses

The equation has one solution: x=3.
The equation has one solution: x equals 3 .

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

The equation has no solution.
The equation has no solution.

The equation has one solution: x=−3.

Answer 1

To solve this equation, we can start by simplifying both sides:

3(x + 2) - 6 = 3x

Distribute 3 on the left side:

3x + 6 - 6 = 3x

Combine like terms:

3x = 3x

We can see that the variable x is present on both sides of the equation. This means that the equation has infinite solutions. The correct response is "The equation has infinite solutions."

Answer 2

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

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

The equation has no solution.
The equation has no solution.

The equation has one solution: x=−10.

Answer 3

Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6 (1 point)
Responses

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

The equation has no solution.
The equation has no solution.

The equation has one solution: x=6.
The equation has one solution: x equals 6 .

The equation has one solution: x=10.