Question 1: The given equation has one solution. Therefore, the correct answer is A) one solution.
Question 2: The equation that has infinitely many solutions is C) 11x − 2x + 15 = 8 + 7 + 9x.
Linear Equations in One Variable
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 solutionone solution
B two solutionstwo solutions
C infinitely many solutionsinfinitely many solutions
D no solutionno 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 + 12x
3 answers
are you sure
I apologize for the confusion in my previous response. Let's reevaluate the equations.
Question 1: By simplifying the equation 7x − 6 + 3 = 5x + 2x + 5, we get 7x - 3 = 7x + 5. When we further simplify it, we get -3 = 5 which is not true. This means that there are no solutions for the given equation. Therefore, the correct answer is D) no solution.
Question 2: Let's evaluate the given options:
A) 9x − 3 = 3x + 6x + 2 + 3: This equation can be simplified to 9x - 3 = 9x + 5, which is not true. Therefore, it does not have infinitely many solutions.
B) 12(x + 8) = 11x − 5: This equation can be simplified to 12x + 96 = 11x - 5. By further simplification, we get x = -101. This is a specific value for x, so it does not have infinitely many solutions.
C) 11x − 2x + 15 = 8 + 7 + 9x: This equation can be simplified to 9x + 15 = 15 + 9x, which is true for all values of x. This means that the equation has infinitely many solutions.
D) 5x − 8 = 11 − 7x + 12x: This equation can be simplified to 5x - 8 = 11 + 5x, which is not true. Therefore, it does not have infinitely many solutions.
Therefore, the correct answer is C) 11x − 2x + 15 = 8 + 7 + 9x, which has infinitely many solutions.
Question 1: By simplifying the equation 7x − 6 + 3 = 5x + 2x + 5, we get 7x - 3 = 7x + 5. When we further simplify it, we get -3 = 5 which is not true. This means that there are no solutions for the given equation. Therefore, the correct answer is D) no solution.
Question 2: Let's evaluate the given options:
A) 9x − 3 = 3x + 6x + 2 + 3: This equation can be simplified to 9x - 3 = 9x + 5, which is not true. Therefore, it does not have infinitely many solutions.
B) 12(x + 8) = 11x − 5: This equation can be simplified to 12x + 96 = 11x - 5. By further simplification, we get x = -101. This is a specific value for x, so it does not have infinitely many solutions.
C) 11x − 2x + 15 = 8 + 7 + 9x: This equation can be simplified to 9x + 15 = 15 + 9x, which is true for all values of x. This means that the equation has infinitely many solutions.
D) 5x − 8 = 11 − 7x + 12x: This equation can be simplified to 5x - 8 = 11 + 5x, which is not true. Therefore, it does not have infinitely many solutions.
Therefore, the correct answer is C) 11x − 2x + 15 = 8 + 7 + 9x, which has infinitely many solutions.