Question

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

5(2x + 2) - 7x = 3x + 6 (1 point)

The equation has one solution: x = 6

The equation has infinite solutions.

The equation has one solution: x = 10

The equation has no solution.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the given equation, we simplify both sides:

5(2x + 2) - 7x = 3x + 6
10x + 10 - 7x = 3x + 6
3x + 10 = 3x + 6

We notice that there is a 3x term on both sides of the equation. Subtracting 3x from both sides gives us:

10 = 6

This is clearly not true. Therefore, the equation has no solution. 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 for x.

Let's simplify the equation step by step:

Start with the given equation: 5(2x + 2) - 7x = 3x + 6

First, distribute 5 to the terms inside the parentheses: 10x + 10 - 7x = 3x + 6

Combine like terms on both sides of the equation: (10x - 7x) + 10 = 3x + 6

Simplify: 3x + 10 = 3x + 6

Next, subtract 3x from both sides of the equation to eliminate the variable: 3x - 3x + 10 = 3x - 3x + 6

Simplify: 10 = 6

Since this equation simplifies to 10 = 6, which is not a true statement, we conclude that there is no solution to the equation.

Therefore, the equation has no solution.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation 5(2x + 2) - 7x = 3x + 6, we'll begin by simplifying both sides of the equation:

First, distribute the 5 to the terms inside the parentheses:
10x + 10 - 7x = 3x + 6

Next, combine like terms on both sides of the equation:
(10x - 7x) + 10 = (3x) + 6
3x + 10 = 3x + 6

Now, we'll isolate the variable x by subtracting 3x from both sides:
(3x - 3x) + 10 = (3x - 3x) + 6
10 = 6

Since the equation 10 = 6 is not true, we have arrived at a contradiction.

Therefore, the equation does not have a solution. The correct answer is: The equation has no solution.