Which of the following numbers is not a solution to the inequality `6x-9 ge 7x-5`?

Options

A. `-8`
B. `-5`
C. `-4`
D. `-2`

Explanation

To solve the inequality \(6x - 9 \geq 7x - 5\) and determine which of the provided options is not a solution, we will follow these steps:

### Step 1: Rearranging the Inequality
Start with the given inequality:
\[ 6x - 9 \geq 7x - 5 \]
We want to isolate \(x\). First, we will move \(7x\) to the left side and \(-9\) to the right side.

### Step 2: Move Terms
Subtract \(7x\) from both sides:
\[ 6x - 7x - 9 \geq -5 \]
This simplifies to:
\[ -x - 9 \geq -5 \]

### Step 3: Isolate \(x\)
Next, add \(9\) to both sides:
\[ -x \geq -5 + 9 \]
This simplifies to:
\[ -x \geq 4 \]

### Step 4: Multiply by -1
To solve for \(x\), multiply both sides by \(-1\). Remember that this reverses the inequality sign:
\[ x \leq -4 \]

### Step 5: Solution Set
The solution to the inequality is:
\[ x \leq -4 \]
This means \(x\) can take any value less than or equal to \(-4\).

### Step 6: Analyze Options
Now, we need to check the provided options to see which one does not satisfy the inequality \(x \leq -4\).

Assuming the options are:
1. \(-8\)
2. \(-5\)
3. \(-4\)
4. \(-2\)

- **For \(-8\)**: \(-8 \leq -4\) (True)
- **For \(-5\)**: \(-5 \leq -4\) (True)
- **For \(-4\)**: \(-4 \leq -4\) (True)
- **For \(-2\)**: \(-2 \leq -4\) (False)

### Conclusion
The number that is not a solution to the inequality \(6x - 9 \geq 7x - 5\) is:
\[ \boxed{-2} \]