Question

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

The equation has one solution x=-1

The equation has infinite solutions

The equation has no solution

The equation has one solution x = -3

Answer 1

Let's start by solving the equation:

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

First, distribute the 3 on the right-hand side:

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

Now, combine like terms on the right side:

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

This simplifies to:

\[ 11x = 11x - 3 \]

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

\[ 11x - 11x = 11x - 3 - 11x \]
\[ 0 = -3 \]

This statement, \(0 = -3\), is a contradiction and is not true. Therefore, this indicates that there are **no solutions** to the equation.

So the answer is: **The equation has no solution.**