Question

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

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

The equation has one solution: x=10.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for x, we can simplify the equation first:

5(2x + 2) - 7x = 3x + 6

First, distribute the 5:

10x + 10 - 7x = 3x + 6

Combine like terms:

10x - 7x + 10 = 3x + 6

3x + 10 = 3x + 6

Now, subtract 3x from both sides:

3x - 3x + 10 = 3x - 3x + 6

10 = 6

Since this results in a false statement (10 is not equal to 6), there is no solution to this equation.

Therefore, the correct answer is:
The equation has no solution.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine if the equation has one, none, or infinite solutions, we need to solve it for x.

5(2x + 2) - 7x = 3x + 6

First, distribute the 5 to both terms inside the parentheses:

10x + 10 - 7x = 3x + 6

Combine like terms on both sides:

(10x - 7x) + 10 = 3x + 6

3x + 10 = 3x + 6

Subtract 3x from both sides:

10 = 6

This is not a true statement. When an equation leads to a false statement, it means that there are no solutions. Therefore, the equation has no solution.