Solve for x to determine if the equation has one, none, or infinite solutions.

Question

11x=3(7x−1)−10x (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=−1.

Answer 1

To determine if the equation has one, none, or infinite solutions, we need to solve for x.

11x = 3(7x - 1) - 10x
11x = 21x - 3 - 10x
11x = 11x - 3
0 = -3

This is a contradiction, as 0 cannot equal -3. Therefore, the equation has no solution. The correct response is: The equation has no solution.

Answer 2

Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6 (1 point)
Responses

The equation has no solution.
The equation has no solution.

The equation has one solution: x=1.
The equation has one solution: x equals 1 .

The equation has one solution: x=0.
The equation has one solution: x equals 0 .

The equation has infinite solutions.

Answer 3

To determine if the equation has one, none, or infinite solutions, we need to solve for x.

5(2x + 2) - 4 = 2x + 6
10x + 10 - 4 = 2x + 6
10x + 6 = 2x + 6
10x - 2x = 6 - 6
8x = 0
x = 0

Therefore, the equation has one solution: x = 0. The correct response is: The equation has one solution: x=0.