Which of the following is an example of an equation with no solution?(1 point)
Responses
3x+4=4x+3
4x+3=3x+3
3x+4=3x+3
3x+4=3x+4
3x+4=3x+4 is an example of an equation with no solution.
why?
The equation 3x+4=3x+4 is an example of an equation with no solution because when you simplify it, you end up with 4=4, which is a true statement. This means that the equation is true for all values of x, and there is not a specific value of x that will make the equation false. Therefore, there is no unique solution to the equation.
what about 3x+4=3x+3?
Apologies for the confusion. 3x+4=3x+3 is an example of an equation with no solution.
When we simplify the equation by subtracting 3x from both sides, we get:
4 = 3
This is not a true statement because 4 is not equal to 3. Therefore, there is no value of x that will make the equation true, and the equation has no solution.
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
4x+3=4x+3
3x+4=3x+4
3x+4=3x+3
3x+4=4x+3
3x+4=3x+4 is an example of an equation with exactly one solution.
3(x+2)−6=3x
The equation 3(x+2)−6=3x is an example of an equation with exactly one solution.
To solve this equation, we can distribute the 3 to the terms inside the parentheses:
3x + 6 - 6 = 3x
This simplifies to:
3x = 3x
In this case, we can subtract 3x from both sides, resulting in:
0 = 0
This is a true statement, which means that the equation is satisfied for all values of x. Therefore, there is exactly one solution to this equation, which is that x can be any real number.
To determine which of the given equations has no solution, we need to compare the coefficients of x on both sides of the equation.
For the equation 3x + 4 = 4x + 3, we can see that the coefficients of x on both sides are 3 and 4, respectively. These coefficients are not equal, so this equation does not have a solution.
For the equation 4x + 3 = 3x + 3, the coefficients of x on each side are 4 and 3, respectively. Again, these coefficients are not equal, so this equation also does not have a solution.
For the equation 3x + 4 = 3x + 3, we have the same coefficient of x (3) on both sides of the equation. However, even though the coefficients are equal, we still need to consider the constants on both sides. In this case, the constants are 4 and 3, respectively. They are not equal, so this equation does not have a solution either.
Finally, for the equation 3x + 4 = 3x + 4, we have the same coefficient of x (3) and the same constant (4) on both sides of the equation. Since the coefficients and constants are equal, this equation has infinitely many solutions.
Therefore, the answer is the first option: 3x + 4 = 4x + 3. It is the only equation among the options that has no solution.