Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( r > 9 \)
Solution
Sure, let's solve the inequality step by step.
**Given Inequality:**
\[ 7r > 9 + 6r \]
**Step 1: Subtract \(6r\) from both sides to isolate terms containing \(r\) on one side.**
\[
7r - 6r > 9 + 6r - 6r
\]
\[
r > 9
\]
**Solution:**
\[
r > 9
\]
**Interpretation:**
Any real number \(r\) that is greater than 9 satisfies the inequality \(7r > 9 + 6r\).
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Simplify this solution Beyond the Answer
To solve the inequality \( 7r > 9 + 6r \), let's start by isolating the variable on one side. Subtract \(6r\) from both sides to get \(7r - 6r > 9\), which simplifies to \(r > 9\). Now you've got a simple inequality: any value of \(r\) greater than 9 will make the original inequality true. So \(r\) can be 10, 11, or even a juicy decimal like 9.5! Remember, when dealing with inequalities, you can treat them similarly to equations, but be careful to reverse the inequality sign when multiplying or dividing by a negative number—like flipping pancakes at breakfast!
