The solution set of the inequalities `3x-7gt2(x-6)` and `6-xgt11-2x,` is

Options

A. `(-5,oo)`
B. `[5,oo)`
C. `(5,oo)`
D. `[-5,oo)`

Answer

To solve the inequalities \(3x - 7 > 2(x - 6)\) and \(6 - x > 11 - 2x\), we will break it down into steps.

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

1. Distribute on the right side:
\[ 3x - 7 > 2x - 12 \]

2. Subtract \(2x\) from both sides:
\[ 3x - 2x - 7 > -12 \]
\[ x - 7 > -12 \]

3. Add \(7\) to both sides:
\[ x > -12 + 7 \]
\[ x > -5 \]

### Step 2: Solve the second inequality \(6 - x > 11 - 2x\)

1. Rearranging gives:
\[ 6 - x > 11 - 2x \]

2. Add \(2x\) to both sides:
\[ 6 + x > 11 \]

3. Subtract \(6\) from both sides:
\[ x > 11 - 6 \]
\[ x > 5 \]

### Step 3: Combine the results from both inequalities

From the first inequality, we have:
\[ x > -5 \]
From the second inequality, we have:
\[ x > 5 \]

### Step 4: Determine the common solution set

The more restrictive condition is \(x > 5\). Therefore, the solution set for the combined inequalities is:
\[ x > 5 \]

### Final Answer

The solution set of the inequalities is:
\[ (5, \infty) \]