Which of the following is an example of an equation with no solution?(1 point)
Responses
4x+3=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=3x+4
3x+4=3x+4 is an example of an equation with infinitely many solutions, not no solution.
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
4x+3=4x+3
4 x plus 3 equals 4 x plus 3
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=4x+3
3x+4=4x+3 is an example of an equation with exactly one solution.
Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x(1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has one solution: x=3.
To solve the equation 3(x+2)-6=3x, we can simplify the equation:
3x + 6 - 6 = 3x
3x = 3x
The variables cancel out, leaving us with an identity: 3x = 3x. This means that the equation has infinitely many solutions. Therefore, the correct response is "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
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−10.
To solve the equation 4x = 3(x+5) - 15, we can simplify the equation:
4x = 3x + 15 - 15
4x = 3x
The variables cancel out, leaving us with an identity: 4x = 4x. This means that the equation has infinitely many solutions. Therefore, the correct response is "The equation has infinite solutions."
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6(1 point)
Responses
The equation has one solution: x=6.
The equation has one solution: x equals 6 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
The equation has no solution.
The equation has one solution: x=10.
To solve the equation 5(2x+2) - 7x = 3x + 6, we can simplify the equation:
10x + 10 - 7x = 3x + 6
3x + 10 = 3x + 6
3x - 3x = 6 - 10
0 = -4
The equation simplifies to 0 = -4, which is not true. This means that there is no solution for x that satisfies the equation. Therefore, the correct response is "The equation has no solution."
To determine which of the equations has no solution, we need to compare the coefficients and constants on both sides of the equation.
Looking at the options:
1) 4x + 3 = 3x + 3
2) 3x + 4 = 4x + 3
3) 3x + 4 = 3x + 3
4) 3x + 4 = 3x + 4
In equations 1, 2, and 4, the coefficients and constants are the same on both sides of the equations. This means that they are equivalent and have an infinite number of solutions.
However, in equation 3, the coefficients are the same, but the constant on the left side (4) is greater than the constant on the right side (3). This creates a contradiction, as the equation states that the two expressions are equal, but they cannot be when the constants are not the same. Therefore, equation 3 has no solution.
So the answer is: 3x + 4 = 3x + 3.