Let's solve the equation:

\[
3r + 7 = 10r + 20
\]

### Step 1: Move all terms involving \(r\) to one side and constants to the other.
Subtract \(3r\) from both sides:

\[
7 = 10r - 3r + 20
\]

Simplify:

\[
7 = 7r + 20
\]

### Step 2: Isolate the variable term.
Subtract 20 from both sides:

\[
7 - 20 = 7r
\]

Simplify:

\[
-13 = 7r
\]

### Step 3: Solve for \(r\).
Divide both sides by 7:

\[
r = \frac{-13}{7}
\]

So, the solution is:

\[
r = -\frac{13}{7}
\]

Would you like more details, or do you have any questions about these steps?

Here are 5 related questions to explore:
1. How do we solve equations with variables on both sides?
2. What happens if there are fractions in the equation?
3. How can we check if our solution is correct?
4. How do you approach an equation with multiple variables?
5. What are some common mistakes to avoid when solving linear equations?

**Tip:** Always double-check your work by plugging your solution back into the original equation!

Discover how to solve the linear equation 3r + 7 = 10r + 20 with this detailed step-by-step guide. This problem introduces key algebraic concepts, including moving variables to one side and isolating terms. Ideal for students in Grades 6-8.

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