Let's solve the equation:

\[
-35 - 7r = -4(5r - 6) + 6
\]

### Step 1: Distribute the \(-4\) on the right-hand side:
\[
-35 - 7r = -4 \times 5r + (-4) \times (-6) + 6
\]
\[
-35 - 7r = -20r + 24 + 6
\]

### Step 2: Simplify the right-hand side:
\[
-35 - 7r = -20r + 30
\]

### Step 3: Add \(7r\) to both sides to move all the \(r\)-terms to one side:
\[
-35 = -20r + 30 + 7r
\]
\[
-35 = -13r + 30
\]

### Step 4: Subtract 30 from both sides to isolate the term with \(r\):
\[
-35 - 30 = -13r
\]
\[
-65 = -13r
\]

### Step 5: Solve for \(r\) by dividing both sides by \(-13\):
\[
r = \frac{-65}{-13} = 5
\]

### Final answer:
\[
r = 5
\]

Would you like more details or further explanation on any step?

Here are some related questions:
1. How do you solve equations with multiple terms on both sides?
2. What happens when you distribute negative numbers in an equation?
3. How do you isolate variables in an equation?
4. What are the general steps to solve linear equations?
5. How do you check if your solution to an equation is correct?

**Tip:** Always simplify each side of the equation as much as possible before trying to isolate the variable.

Learn how to solve the linear equation -35 - 7r = -4(5r - 6) + 6 with a step-by-step breakdown. This solution demonstrates the use of the distributive property, simplifying both sides, and isolating variables. Suitable for students in Grades 8-10.

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