Question

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

Answer 1

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:

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

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

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

Now we have:

\[
11x = 11x - 3
\]

3. 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.