`3x - 7 gt 2 ( x - 6 ), 6 - x gt 11 - 2x `

Explanation

To solve the given inequalities step by step, we will break down each inequality and find the solution.

### Step 1: Solve the first inequality
The first inequality is:
\[ 3x - 7 > 2(x - 6) \]

**Step 1.1:** Expand the right side:
\[ 3x - 7 > 2x - 12 \]

**Step 1.2:** Rearrange the inequality by moving \(2x\) to the left side and \(-7\) to the right side:
\[ 3x - 2x > -12 + 7 \]

**Step 1.3:** Simplify both sides:
\[ x > -5 \]

### Step 2: Solve the second inequality
The second inequality is:
\[ 6 - x > 11 - 2x \]

**Step 2.1:** Rearrange the inequality by moving \(-2x\) to the left side and \(6\) to the right side:
\[ -x + 2x > 11 - 6 \]

**Step 2.2:** Simplify both sides:
\[ x > 5 \]

### Step 3: Combine the results
Now we have two inequalities:
1. \( x > -5 \)
2. \( x > 5 \)

The solution to the system of inequalities is the intersection of both solutions. Since \( x > 5 \) is a stricter condition than \( x > -5 \), the final solution is:
\[ x > 5 \]

### Final Answer
The solution to the given inequalities is:
\[ x \in (5, \infty) \]

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