Question

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

Answer 1

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

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

3x+4=3x+4 is an example of an equation with no solution.

Answer 6

4x+3=4x+3 is an example of an equation with exactly one solution.

Answer 7

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.

Answer 8

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.

Answer 9

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.