Which of the following is an example of an equation with no solution?(1 point)
Responses
3x+4=3x+3
4x+3=3x+3
3x+4=4x+3
3x+4=3x+4
3x+4=3x+4 is an example of an equation with no solution.
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
3x+4=3x+3
3x+4=4x+3
3x+4=3x+4
4x+3=4x+3
4x+3=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 one solution: x=3.
The equation has infinite solutions.
The equation has one solution: x=−3.
The equation has no solution.
Let's solve the equation step by step:
3(x+2) - 6 = 3x
First, distribute the 3:
3x + 6 - 6 = 3x
Simplify and combine like terms:
3x = 3x
At this point, we notice that the variable x cancels out on both sides of the equation. This means that no matter what value we choose for x, both sides of the equation will always be equal. Therefore, the equation has infinite solutions.
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 no solution.
The equation has infinite solutions.
The equation has one solution: x=−10.
The equation has one solution: x=0.
Let's solve the equation step by step:
4x = 3(x+5) - 15
First, distribute the 3:
4x = 3x + 15 - 15
Simplify and combine like terms:
4x = 3x
At this point, we notice that the variable x cancels out on both sides of the equation. This means that no matter what value we choose for x, both sides of the equation will always be equal. Therefore, the equation has infinite solutions.
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 no solution.
The equation has one solution: x=6.
The equation has one solution: x=10.
The equation has infinite solutions.
Let's solve the equation step by step:
5(2x + 2) - 7x = 3x + 6
First, distribute the 5:
10x + 10 - 7x = 3x + 6
Combine like terms:
3x + 10 = 3x + 6
Subtract 3x from both sides:
10 = 6
At this point, we notice that the variables cancel out on both sides of the equation. However, we are left with a false statement (10 = 6), which means there is no solution that satisfies the equation.
The correct response is: The equation has no solution.
To determine which of the given equations has no solution, we need to simplify them and check if they are true or false for any value of x.
Let's simplify each equation:
1) 3x+4=3x+3
Subtracting 3x from both sides gives:
4 = 3
Since 4 is not equal to 3, this equation is false for all values of x.
2) 4x+3=3x+3
Subtracting 3 from both sides gives:
4x = 3x
Subtracting 3x from both sides gives:
x = 0
This equation has a solution, x = 0.
3) 3x+4=4x+3
Subtracting 3x from both sides gives:
4 = x+3
Subtracting 3 from both sides gives:
1 = x
This equation has a solution, x = 1.
4) 3x+4=3x+4
Subtracting 3x from both sides gives:
4 = 4
Since 4 is always equal to 4, this equation is true for all values of x.
Therefore, the correct answer is the first equation: 3x+4=3x+3. It has no solution.