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

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

1 answer

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

  1. Distribute the 3 in \(3(7x - 1)\):

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

So, now the equation is:

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

  1. Combine like terms on the right-hand side:

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

Now we have:

\[ 11x = 11x - 3 \]

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

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

This simplifies to:

\[ 0 = -3 \]

This is a contradiction, meaning there are no values of \(x\) that can satisfy the equation.

Thus, the equation has none solutions.