The equation given is 7x - 6 + 3 = 5x + 2x + 5.
Simplifying the equation, we have:
7x - 3 = 7x + 5.
If we subtract 7x from both sides of the equation, we get:
-3 = 5.
This equation is not possible since -3 does not equal 5.
Therefore, there is no solution for the given equation.
The correct answer is D) no solution.
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 solution
3 answers
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
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
To determine which equation has infinitely many solutions, we need to find the equation where the variables cancel out and we are left with a true statement.
Let's analyze each of the given equations:
A) 9x - 3 = 3x + 6x + 2 + 39x - 3 = 3x + 6x + 2 + 3
Combining like terms, we have:
9x - 3 = 8x + 5
Subtracting 8x from both sides, we get:
x - 3 = 5
Adding 3 to both sides gives:
x = 8
This equation has a single solution, so it does not have infinitely many solutions.
B) 12(x + 8) = 11x - 5
Expanding the brackets, we have:
12x + 96 = 11x - 5
Subtracting 11x from both sides, we find:
x + 96 = -5
Subtracting 96 from both sides, we get:
x = -101
This equation has a single solution, so it does not have infinitely many solutions.
C) 11x - 2x + 15 = 8 + 7 + 9x
Combining like terms, we have:
9x + 15 = 15 + 9x
Subtracting 9x from both sides, we obtain:
15 = 15
This equation simplifies to 15 = 15, which is true for any value of x. Therefore, this equation has infinitely many solutions.
D) 5x - 8 = 11 - 7x + 12x
Combining like terms, we have:
5x - 8 = 11 + 5x
Subtracting 5x from both sides, we find:
-8 = 11
This equation simplifies to -8 = 11, which is false. Therefore, this equation does not have any solutions.
In conclusion, the equation C) 11x - 2x + 15 = 8 + 7 + 9x has infinitely many solutions.
Let's analyze each of the given equations:
A) 9x - 3 = 3x + 6x + 2 + 39x - 3 = 3x + 6x + 2 + 3
Combining like terms, we have:
9x - 3 = 8x + 5
Subtracting 8x from both sides, we get:
x - 3 = 5
Adding 3 to both sides gives:
x = 8
This equation has a single solution, so it does not have infinitely many solutions.
B) 12(x + 8) = 11x - 5
Expanding the brackets, we have:
12x + 96 = 11x - 5
Subtracting 11x from both sides, we find:
x + 96 = -5
Subtracting 96 from both sides, we get:
x = -101
This equation has a single solution, so it does not have infinitely many solutions.
C) 11x - 2x + 15 = 8 + 7 + 9x
Combining like terms, we have:
9x + 15 = 15 + 9x
Subtracting 9x from both sides, we obtain:
15 = 15
This equation simplifies to 15 = 15, which is true for any value of x. Therefore, this equation has infinitely many solutions.
D) 5x - 8 = 11 - 7x + 12x
Combining like terms, we have:
5x - 8 = 11 + 5x
Subtracting 5x from both sides, we find:
-8 = 11
This equation simplifies to -8 = 11, which is false. Therefore, this equation does not have any solutions.
In conclusion, the equation C) 11x - 2x + 15 = 8 + 7 + 9x has infinitely many solutions.
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