To solve the equation \( 5r - 7 = 2r + 14 \), follow these steps:

1. **Subtract \( 2r \) from both sides** to get all terms involving \( r \) on one side of the equation:
   \[
   5r - 2r - 7 = 14
   \]
   Simplifying, we get:
   \[
   3r - 7 = 14
   \]

2. **Add 7 to both sides** to isolate the term with \( r \):
   \[
   3r = 14 + 7
   \]
   Simplifying, we get:
   \[
   3r = 21
   \]

3. **Divide both sides by 3** to solve for \( r \):
   \[
   r = \frac{21}{3}
   \]
   Simplifying, we get:
   \[
   r = 7
   \]

So, the solution is \( r = 7 \).

Would you like more details on any step, or do you have any questions?

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Here are 5 related questions:

1. How would you solve \( 4r + 3 = 9r - 12 \)?
2. What happens if you subtract \( 14 \) from both sides in the equation \( 5r - 7 = 2r + 14 \)?
3. How do you check if your solution to \( 5r - 7 = 2r + 14 \) is correct?
4. How do you solve the equation \( 7r - 4r + 5 = 3r + 9 \)?
5. What if the equation was \( 5r - 7 = 2r + 14 - r \)? How would the solution change?

**Tip:** Always simplify the equation as much as possible before solving for the variable. This can make the solution process more straightforward.

Learn how to solve the linear equation 5r - 7 = 2r + 14 with a detailed step-by-step solution. This problem covers fundamental algebraic concepts and is suitable for students in Grades 6-8.

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