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+4
3 x plus 4 equals 3 x plus 4
3x+4=3x+3
3x + 4 = 3x + 4
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
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=4x+3
4x + 3 = 4x + 3
4 x plus 3 equals 4 x plus 3
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 negative 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 3 .
1. Expand the left side of the equation: 3x + 3(2) - 6 = 3x + 6 - 6 = 3x
2. Simplify and solve:
3x + 6 - 6 = 3x
3x = 3x
3. This equation indicates that the left side equals the right side for all values of x.
4. The equation has infinite solutions because the equation holds true for all values of x.
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 infinite solutions.
The equation has infinite solutions.
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 no solution.
1. Expand the right side of the equation: 3(x) + 3(5) - 15 = 3x + 15 - 15 = 3x
2. Simplify and solve:
4x = 3x
4x equals 3x
3. As 4 does not equal 3, this is a contradiction.
4. The equation has no solution.
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=10.
The equation has one solution: x equals 10 .
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.
1. Expand the left side of the equation: 5(2x) + 5(2) - 7x = 10x + 10 - 7x = 3x + 10
2. Simplify and solve:
10x + 10 - 7x = 3x + 6
3x + 10 = 3x + 6
3. Subtract 3x from both sides and simplify:
10 = 6
4. The left side of the equation does not equal the right side.
5. The equation has no solution.