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=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=4x+3
3 x plus 4 equals 4 x plus 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?
Responses
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
4x+3=4x+3
4 x plus 3 equals 4 x plus 3
3x+4=3x+4
3x+4=3x+4 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 one solution: x equals 3 .
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 .
Let's solve the equation step by step:
3(x+2) - 6 = 3x
First, we distribute the 3:
3x + 6 - 6 = 3x
Now we simplify:
3x = 3x
The equation remains the same after simplifying. This means that the equation has infinite solutions, as any value of x will satisfy the equation. 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=−10.
The equation has one solution: x equals negative 10 .
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.
Let's solve the equation step by step:
4x = 3(x+5) - 15
First, we distribute the 3:
4x = 3x + 15 - 15
Simplifying, we get:
4x = 3x
At this point, we can subtract 3x from both sides:
4x - 3x = 3x - 3x
This simplifies to:
x = 0
Therefore, the equation has one solution: x = 0. The correct response is:
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
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=10.
The equation has one solution: x equals 10 .
The equation has one solution: x=6.
Let's solve the equation step by step:
5(2x+2) - 7x = 3x + 6
First, we distribute the 5:
10x + 10 - 7x = 3x + 6
Combine like terms:
10 - 6 = 3x + 7x - 10x
4 = 0
Since we have reached a contradiction (4 = 0), there is no solution for the equation. Therefore, the correct response is:
The equation has no solution.
To determine which of the given equations has no solution, you need to compare the coefficients and constants on both sides of the equation.
Let's analyze each equation:
1) 4x+3=3x+3
If we subtract 3x from both sides of the equation, we get 4x - 3x + 3 = 3. Simplifying further, x + 3 = 3. By subtracting 3 from both sides, we have x = 0. Thus, this equation does have a solution.
2) 3x+4=3x+3
If we subtract 3x from both sides of the equation, we get 3x - 3x + 4 = 3. Simplifying further, 4 = 3. However, this creates an inconsistency because 4 is not equal to 3. Therefore, this equation has no solution.
3) 3x+4=4x+3
If we subtract 3x from both sides of the equation, we get 3x - 3x + 4 = 4. Simplifying further, 4 = 4. This equation is consistent because 4 is indeed equal to 4. Thus, this equation does have a solution.
4) 3x+4=3x+4
If we subtract 3x from both sides of the equation, we get 3x - 3x + 4 = 4. Simplifying further, 4 = 4. Similarly to the previous equation, this equation is consistent because 4 is equal to 4. Thus, this equation does have a solution.
From analyzing the given equations, we can conclude that option 2) 3x+4=3x+3 is the example of an equation with no solution.