Let's solve the equation \(-6x = -5(x - 1) - x\).

### Step 1: Distribute the \(-5\) on the right-hand side.
\[
-6x = -5x + 5 - x
\]

### Step 2: Combine like terms on the right-hand side.
\[
-6x = -6x + 5
\]

### Step 3: Add \(6x\) to both sides to eliminate the \(-6x\) on the left-hand side.
\[
0 = 5
\]

### Conclusion:
The equation simplifies to \(0 = 5\), which is a contradiction. This means that there is no solution to the equation. It is an inconsistent equation.

Would you like more details or have any questions?

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Here are five related questions:
1. How can you identify an inconsistent equation before solving?
2. What are the properties of equations with no solutions?
3. Can an equation have infinitely many solutions? If so, how?
4. How would you graphically represent the solution to an inconsistent equation?
5. What happens when solving an equation results in a true statement like \(0 = 0\)?

**Tip:** When solving equations, always look for contradictions or identities to quickly determine if there are no solutions or infinite solutions.

Learn how to solve the equation -6x = -5(x - 1) - x with detailed step-by-step solution. This problem involves linear equations, distributive property, and combining like terms. Suitable for Grades 7-9 students.

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