Question 1
To begin, we can simplify the equation given on the left side:
7x - 6 + 3 = 5x + 2x + 5
7x - 3 = 7x + 5
Next, we can subtract 7x from both sides to eliminate the variable:
-3 = 5
Since -3 does not equal 5, this means that there are no solutions for the given equation.
Therefore, the answer to Question 1 is D) no solution.
Question 2
To determine which equation has infinitely many solutions, we need to find an equation in which the variable cancels out and we are left with a true statement.
Looking at the equation options, we can simplify each one:
A) 9x - 3 = 3x + 6x + 2 + 3
Simplifying this equation, we get:
9x - 3 = 9x + 5
We can subtract 9x from both sides:
-3 = 5
This equation is not true, so it does not have infinitely many solutions.
B) 12(x + 8) = 11x - 5
Expanding the left side of the equation, we get:
12x + 96 = 11x - 5
Simplifying further, we can subtract 11x from both sides:
12x - 11x + 96 = -5
This simplifies to:
x + 96 = -5
Subtracting 96 from both sides, we get:
x = -101
This equation has only one solution, so it does not have infinitely many solutions.
C) 11x - 2x + 15 = 8 + 7 + 9x
Simplifying this equation, we get:
9x + 15 = 15 + 9x
Both sides of the equation are the same, so this equation has infinitely many solutions. This is because any value of x will make the equation true.
D) 5x - 8 = 11 - 7x + 12x
Combining like terms, we get:
5x - 8 = 11 + 5x
Subtracting 5x from both sides, we get:
-8 = 11
This equation is not true, so it does not have infinitely many solutions.
Therefore, the answer to Question 2 is C) 11x - 2x + 15 = 8 + 7 + 9x.
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
the other one
I apologize for the confusion. Let's analyze the options once again:
Question 2:
A) 9x − 3 = 3x + 6x + 2 + 3
Simplifying this equation, we get:
9x - 3 = 9x + 5
Subtracting 9x from both sides, we have:
-3 = 5
This equation is not true, so it does not have infinitely many solutions.
B) 12(x + 8) = 11x − 5
Expanding the left side of the equation, we get:
12x + 96 = 11x - 5
Subtracting 11x from both sides, we have:
12x - 11x + 96 = -5
Simplifying further, we get:
x + 96 = -5
Subtracting 96 from both sides, we get:
x = -101
This equation has only one solution, so it does not have infinitely many solutions.
C) 11x − 2x + 15 = 8 + 7 + 9x
Simplifying this equation, we get:
9x + 15 = 15 + 9x
Both sides of the equation are the same, so this equation has infinitely many solutions. This is because any value of x will make the equation true.
D) 5x − 8 = 11 − 7x + 12x
Combining like terms, we get:
17x - 8 = 11
Adding 8 to both sides, we have:
17x = 19
Dividing by 17, we find:
x = 19/17
This equation has only one solution, so it does not have infinitely many solutions.
Therefore, the answer to Question 2 is C) 11x − 2x + 15 = 8 + 7 + 9x.
Question 2:
A) 9x − 3 = 3x + 6x + 2 + 3
Simplifying this equation, we get:
9x - 3 = 9x + 5
Subtracting 9x from both sides, we have:
-3 = 5
This equation is not true, so it does not have infinitely many solutions.
B) 12(x + 8) = 11x − 5
Expanding the left side of the equation, we get:
12x + 96 = 11x - 5
Subtracting 11x from both sides, we have:
12x - 11x + 96 = -5
Simplifying further, we get:
x + 96 = -5
Subtracting 96 from both sides, we get:
x = -101
This equation has only one solution, so it does not have infinitely many solutions.
C) 11x − 2x + 15 = 8 + 7 + 9x
Simplifying this equation, we get:
9x + 15 = 15 + 9x
Both sides of the equation are the same, so this equation has infinitely many solutions. This is because any value of x will make the equation true.
D) 5x − 8 = 11 − 7x + 12x
Combining like terms, we get:
17x - 8 = 11
Adding 8 to both sides, we have:
17x = 19
Dividing by 17, we find:
x = 19/17
This equation has only one solution, so it does not have infinitely many solutions.
Therefore, the answer to Question 2 is C) 11x − 2x + 15 = 8 + 7 + 9x.