Question

Consider the equation 7x − 6 + 3 = 5x + 2x + 5.

Question 1
Which BEST describes the number of solutions for the given equation?
Responses
A one solution
B two solutions
C infinitely many solutions
D no solution
Question 2
Which equation has infinitely many solutions?
Responses
A 9x − 3 = 3x + 6x + 2 + 39x − 3 = 3x + 6x + 2 + 3
B 12(x + 8) = 11x − 512(x + 8) = 11x − 5
C 11x − 2x + 15 = 8 + 7 + 9x11x − 2x + 15 = 8 + 7 + 9x
D 5x − 8 = 11 − 7x + 12x5x − 8 = 11 − 7x + 12x

© Progress Learning 2023, All Rights Reserved.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Question 1:

The equation 7x − 6 + 3 = 5x + 2x + 5 can be simplified to 7x - 3 = 7x + 5. Combining like terms, we get -3 = 5, which is not true. Therefore, the equation has no solution. The correct answer is D) no solution.

Question 2:
To determine which equation has infinitely many solutions, we need to look for an equation where the variables cancel out and the equation becomes a true statement regardless of the value of x. Let's examine the options:

A) 9x − 3 = 3x + 6x + 2 + 39x − 3 = 3x + 6x + 2 + 3
Both equations have the same expression on both sides of the equal sign. This means that the variables will cancel out, and the equation will always be true. Therefore, option A) has infinitely many solutions.

B) 12(x + 8) = 11x − 5
C) 11x − 2x + 15 = 8 + 7 + 9x
D) 5x − 8 = 11 − 7x + 12x
None of these options have the property where the variables cancel out in the equation, so they do not have infinitely many solutions.

Therefore, the correct answer is A) 9x − 3 = 3x + 6x + 2 + 3.

Answer 2

are you sure?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. Let's reconsider the solutions:

Question 1:
The equation 7x - 6 + 3 = 5x + 2x + 5 can be simplified to 7x - 3 = 7x + 5. By subtracting 7x from both sides, we will get -3 = 5, which is not correct. This means that the equation has no solution. The correct answer is D) no solution.

Question 2:
Let's reevaluate the options:

A) 9x − 3 = 3x + 6x + 2 + 3
Simplifying this equation, we get 9x - 3 = 9x + 5. By subtracting 9x from both sides, we have -3 = 5, which is not true. This means that the equation does not have infinitely many solutions.

B) 12(x + 8) = 11x − 5
Simplifying this equation, we get 12x + 96 = 11x - 5. By subtracting 11x from both sides, we have x + 96 = -5. By subtracting 96 from both sides, we get x = -101. This means that the equation has one solution, x = -101.

C) 11x − 2x + 15 = 8 + 7 + 9x
Simplifying this equation, we get 9x + 15 = 15 + 9x. By subtracting 9x from both sides, we have 15 = 15. This is a true statement. This means that the equation has infinitely many solutions.

D) 5x − 8 = 11 − 7x + 12x
Simplifying this equation, we get 15x - 8 = 11. By adding 8 to both sides, we have 15x = 19. By dividing both sides by 15, we get x = 19/15. This means that the equation has one solution, x = 19/15.

Therefore, the correct answer for Question 2 is C) 11x − 2x + 15 = 8 + 7 + 9x.