Question

Solve for z to determine if the equation has one, none, or infinite solutions.
11x = 3 (7x - 1) - 10x
• The equation has infinite solutions.
O The equation has one solution: x = -3.
O The equation has no solution.
O The equation has one solution: x = -1.

Answer 1

To determine if the equation has one, none, or infinite solutions, we will simplify the given equation:

1. Start with the equation:
\[
11x = 3(7x - 1) - 10x
\]

2. Distribute the \(3\) on the right side:
\[
11x = 21x - 3 - 10x
\]

3. Combine like terms on the right side:
\[
11x = (21x - 10x) - 3 \\
11x = 11x - 3
\]

4. Subtract \(11x\) from both sides:
\[
11x - 11x = 11x - 11x - 3 \\
0 = -3
\]

The equation \(0 = -3\) is a contradiction, which means there are no values of \(x\) that can satisfy this equation.

Therefore, the equation has **no solution**.

**Final answer: The equation has no solution.**