Let's solve the equation step by step:

\[
36 - 7x = -7(x - 5)
\]

### Step 1: Expand both sides
Expand the right-hand side:

\[
36 - 7x = -7(x) + (-7)(-5)
\]

\[
36 - 7x = -7x + 35
\]

### Step 2: Combine like terms
Now, move all the constants to one side and the terms with \(x\) to the other:

\[
36 - 35 = -7x + 7x
\]

\[
1 = 0
\]

### Conclusion:
This equation leads to a contradiction, meaning there is **no solution**. The system is inconsistent.

Let me know if you want further explanation, or if you'd like to try more problems.

Here are 5 related questions to explore:
1. Solve the equation: \(2x + 3 = 5x - 7\).
2. What happens when you solve an equation with infinitely many solutions?
3. How do you know when an equation has no solution?
4. Can a linear equation have exactly two solutions?
5. Solve the equation: \(4(x - 2) = 2(2x + 5)\).

**Tip**: Always check for contradictions or identities when solving equations—they reveal important properties about the system.

Learn how to solve the linear equation 36 - 7x = -7(x - 5) step-by-step. This problem demonstrates key algebraic concepts, including the distributive property and inconsistent systems, where no solution exists. Suitable for students in Grades 8-10.

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