We are given the equation:

\[
r - 5 = 1 + 4r
\]

Let's solve it step by step.

### Step 1: Move all terms involving \(r\) to one side
Subtract \(4r\) from both sides:

\[
r - 4r - 5 = 1
\]

This simplifies to:

\[
-3r - 5 = 1
\]

### Step 2: Isolate the \(r\) term
Add 5 to both sides:

\[
-3r = 6
\]

### Step 3: Solve for \(r\)
Divide both sides by \(-3\):

\[
r = \frac{6}{-3} = -2
\]

### Final Answer:
\[
r = -2
\]

Would you like a detailed explanation on any part of the solution? 

Here are 5 related questions you might find helpful:
1. How do you solve multi-step linear equations?
2. Can you explain how to check if the solution is correct?
3. What happens if the variable appears on both sides in more complicated equations?
4. How do you solve equations with fractions?
5. What if the equation has no solution or infinitely many solutions?

**Tip:** When solving linear equations, always simplify both sides as much as possible before trying to isolate the variable!

Discover how to solve the linear equation r - 5 = 1 + 4r with a clear, step-by-step guide. This problem highlights key algebraic skills, including moving terms, combining like terms, and isolating the variable. Ideal for students in Grades 6-8 who are learning about solving equations with variables on both sides.

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