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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 infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=−3
.
The equation has one solution: x equals negative 3 .

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

The equation has one solution: x=−1
.

1 answer

Let's solve the equation step by step:

The equation given is:

\[ 11x = 3(7x - 1) - 10x \]

First, simplify the right side:

  1. Distribute the 3 on the right side: \[ 3(7x - 1) = 21x - 3 \]

Now, we can rewrite the equation:

\[ 11x = 21x - 3 - 10x \]

  1. Combine like terms on the right side: \[ 21x - 10x = 11x \] So, we have: \[ 11x = 11x - 3 \]

Next, we subtract \(11x\) from both sides:

\[ 11x - 11x = 11x - 11x - 3 \]

This simplifies to:

\[ 0 = -3 \]

This statement is not true. Since we arrived at a contradiction, it means that the original equation has no solution.

Thus, the correct response is:

The equation has no solution.