Question

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

5(2x+2)−7x=3x+6

A. The equation has no solution.

B. The equation has infinite solutions.

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

D. The equation has one solution: x=10

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for x, we can start by simplifying the equation by multiplying the numbers outside the parentheses:

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

Next, we can combine like terms by moving the variables to one side of the equation and the constants to the other side:

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

-3x = -4

Now, we can solve for x by dividing both sides of the equation by -3:

x = (-4)/(-3)

x = 4/3

Since x is not a whole number, the equation has no solution.

Therefore, the correct answer is:

A. 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 will solve it step by step.

Given equation:
5(2x + 2) - 7x = 3x + 6

Step 1: Distribute the 5 on the left side of the equation:
10x + 10 - 7x = 3x + 6

Step 2: Combine like terms on both sides of the equation:
(10x - 7x) + 10 = 3x + 6
3x + 10 = 3x + 6

Step 3: Move the 3x on the right side of the equation to the left side by subtracting 3x from both sides:
3x - 3x + 10 = 3x - 3x + 6
10 = 6

Step 4: Analyzing the equation, we reach a contradiction where 10 is not equal to 6. Therefore, there is no possible value of x that will make this equation true.

Thus, the equation has no solution.

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