10. After pitching $$ 6 \frac{3}{3} $$ innings in his latest game, Barron has pitched more innings than his $$ 82 \frac{1}{3} $$ innings pitched tast season. How many innings, $$ x $$, might he have pitched before his latest game? Write an inequality to represent the situation. Solve your inequality.

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UpStudy AI · Accepted Answer

Let's break down the problem step by step.

### **Understanding the Problem**
- **Latest Game:** Barron pitched $$ 6 \frac{3}{3} $$ innings.
- **Total After Latest Game:** This total should exceed his previous season's innings of $$ 82 \frac{1}{3} $$ innings.
- **Goal:** Find the number of innings, $$ x $$, Barron might have pitched **before** his latest game.

### **Simplifying Mixed Numbers**
First, simplify the mixed numbers to improper fractions or decimal form for easier calculation:
- $$ 6 \frac{3}{3} = 6 + 1 = 7 $$ innings
- $$ 82 \frac{1}{3} = 82.333\ldots $$ innings

### **Setting Up the Inequality**
Let $$ x $$ represent the number of innings pitched **before** the latest game. After pitching 7 innings in the latest game, his total innings become:
$$ x + 7 $$

According to the problem, this total is **more than** $$ 82 \frac{1}{3} $$ innings:
$$ x + 7 > 82 \frac{1}{3} $$

### **Solving the Inequality**
Subtract 7 from both sides to isolate $$ x $$:
$$
\begin{align*}
x + 7 &> 82 \frac{1}{3} \
x &> 82 \frac{1}{3} - 7 \
x &> 75 \frac{1}{3}
\end{align*}
$$

### **Conclusion**
Barron must have pitched **more than** $$ 75 \frac{1}{3} $$ innings before his latest game.

### **Final Answer**
An inequality is x + 7 > 82 1⁄3. Solving gives x > 75 1⁄3 innings pitched before the latest game.
The inequality is $$ x + 7 > 82 \frac{1}{3} $$. Solving this gives $$ x > 75 \frac{1}{3} $$ innings pitched before the latest game.

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