Which of the following is an example of an equation with no solution?(1 point)
Responses
A. 3x + 4 = 3x + 4
B. 4x + 3 = 3x + 3
C. 3x + 4 = 4x + 3
D. 3x + 4 = 3x + 3
D. 3x + 4 = 3x + 3
With exactly one solution:
A. 3x + 4 = 3x + 3
B. 3x + 4 = 3x + 4
C. 4x + 3 = 4x + 3
D. 3x + 4 = 4x + 3
B. 3x + 4 = 3x + 4
Solve for x to determine if the equation has one, none, or infinite solutions.
3 ( x + 2 ) − 6 = 3x (1 point)
Responses
A. The equation has no solution.
B. The equation has one solution: x=3.
C. The equation has one solution: x=−3.
D. The equation has infinite solutions.
To solve the equation, we first distribute the 3 to the terms inside the parentheses:
3x + 6 - 6 = 3x
We can simplify it further by canceling out the 6 terms:
3x = 3x
Now, we can subtract 3x from both sides to isolate x:
3x - 3x = 0
This simplifies to:
0 = 0
This means that the equation is true for any value of x. Therefore, the equation has infinite solutions.
D. The equation has infinite solutions.
Solve for x to determine if the equation has one, none, or infinite solutions.
4x = 3 ( x + 5 ) − 15 (1 point)
Responses
A. The equation has one solution: x=0.
B. The equation has one solution: x=−10.
C. The equation has infinite solutions.
D. The equation has no solution.
To solve the equation, we can start by distributing 3 and -15 to the terms inside the parentheses:
4x = 3x + 15 - 15
Simplifying further:
4x = 3x
We can now subtract 3x from both sides to isolate x:
4x - 3x = 0
Simplifying:
x = 0
Therefore, the equation has one solution: x = 0.
A. The equation has one solution: x=0.
Solve for x to determine if the equation has one, none, or infinite solutions.
5 ( 2x + 2 ) − 7x = 3x + 6 (1 point)
Responses
A. The equation has one solution: x=6.
B. The equation has one solution: x=10.
C. The equation has infinite solutions.
D. The equation has no solution.
To solve the equation, we can start by distributing 5 to the terms inside the parentheses:
10x + 10 - 7x = 3x + 6
Simplifying further:
3x + 10 = 3x + 6
Next, we can subtract 3x from both sides to isolate the x term:
10 = 6
This equation is not true, and there is no value of x that would make it true. Therefore, the equation has no solution.
D. The equation has no solution.
To determine which of the given equations has no solution, we need to examine the coefficients and constants on both sides of the equation.
Let's go through each option one by one:
A. 3x + 4 = 3x + 4
In this equation, you can see that the coefficients on both sides (3) and the constants (4) are equal. So, this equation is consistent and true for all values of x. Hence, it has infinitely many solutions.
B. 4x + 3 = 3x + 3
In this equation, the coefficients on both sides are different, but the constants are equal. By subtracting 3x from both sides, we get x = 0. This means the equation has a single solution.
C. 3x + 4 = 4x + 3
In this equation, the coefficients are different, and the constants are different as well. By subtracting 3x from both sides and simplifying, we get x = 1. This means the equation has a single solution.
D. 3x + 4 = 3x + 3
In this equation, the coefficients on both sides are equal, but the constants are different. By subtracting 3 from both sides, we get 4 = 3, which is not true. This implies that no value of x can make the equation true. Therefore, this equation has no solution.
Thus, the equation that has no solution is option D: 3x + 4 = 3x + 3.