Solve for x

Question

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

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

The equation has infinite solutions.
The equation has infinite solutions.

The equation has no solution.

Answer 1

Let's solve the equation step by step:

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

First, distribute the 3 on the right side: \[ 11x = 21x - 3 - 10x \]

Now, simplify the right side: \[ 11x = 21x - 10x - 3 \] \[ 11x = 11x - 3 \]

Next, subtract \(11x\) from both sides: \[ 11x - 11x = 11x - 11x - 3 \] \[ 0 = -3 \]

This statement, \(0 = -3\), is false. This indicates that the equation has no solution.

Conclusion: The equation has no solution.