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

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

answers:

The equation has no solutions

The equation has infinte solutions

The equation has one solution: x = -3

The equation has one solution: x = -1

3 answers

To solve the equation \( 11x = 3 (7x - 1) - 10x \), let's first simplify the right-hand side.

  1. Distribute \(3\) in \(3(7x - 1)\): \[ 3(7x - 1) = 21x - 3 \]

  2. Substitute back into the equation: \[ 11x = 21x - 3 - 10x \]

  3. Simplify the right-hand side: \[ 21x - 10x = 11x \] So, the equation becomes: \[ 11x = 11x - 3 \]

  4. Now, subtract \(11x\) from both sides: \[ 11x - 11x = 11x - 11x - 3 \] This simplifies to: \[ 0 = -3 \]

Since \(0 = -3\) is a contradiction, this indicates that there are no solutions to the equation.

Thus, the answer is: The equation has no solutions.

are you sure

Yes, I am sure. Let's go through the steps again to ensure clarity:

We started with the equation:

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

  1. First, distribute the \(3\) on the right side:

\[ 3(7x - 1) = 21x - 3 \]

So the equation now looks like:

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

  1. Next, simplify the right side by combining like terms:

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

Now we have:

\[ 11x = 11x - 3 \]

  1. Subtract \(11x\) from both sides:

\[ 0 = -3 \]

This is a contradiction since it's impossible for \(0\) to equal \(-3\).

Thus, the conclusion is that the equation has no solutions.

If you have any further questions or need more clarification, feel free to ask!