Question

Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x (1 point)
Responses

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

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

Answer 1

To solve the equation \( 11x = 3(7x - 1) - 10x \), let's simplify it step by step.

1. Distributing \( 3 \) on the right side:
\[
3(7x - 1) = 21x - 3
\]
So, the equation now reads:
\[
11x = 21x - 3 - 10x
\]

2. Combine like terms on the right side:
\[
21x - 10x = 11x
\]
Thus, the equation simplifies to:
\[
11x = 11x - 3
\]

3. To isolate \( x \), subtract \( 11x \) from both sides:
\[
11x - 11x = 11x - 11x - 3
\]
This results in:
\[
0 = -3
\]

Since \( 0 = -3 \) is a false statement, this means there are **no solutions** to the equation.

Therefore, the answer is:
The equation has no solution.