Which of the following numbers is NOT a solution of the inequality `7-5xle-3(x-5)`?

Options

A. `-5`
B. `-4`
C. `-2`
D. `1`

Answer

To solve the inequality \( 7 - 5x \leq -3(x - 5) \), we will follow these steps:

### Step 1: Expand the right side of the inequality
Start by distributing \(-3\) on the right side:
\[ 7 - 5x \leq -3x + 15 \]

### Step 2: Move all terms involving \(x\) to one side
Add \(3x\) to both sides to combine \(x\) terms:
\[ 7 - 5x + 3x \leq 15 \]
This simplifies to:
\[ 7 - 2x \leq 15 \]

### Step 3: Isolate the \(x\) term
Subtract \(7\) from both sides:
\[ -2x \leq 15 - 7 \]
This simplifies to:
\[ -2x \leq 8 \]

### Step 4: Divide by \(-2\)
When dividing by a negative number, remember to reverse the inequality sign:
\[ x \geq -4 \]

### Conclusion
The solution to the inequality is:
\[ x \geq -4 \]

### Step 5: Identify which option is NOT a solution
Now, we need to check which of the given options does not satisfy \(x \geq -4\).

Assuming the options are:
- A) -5
- B) -4
- C) 0
- D) 5

From our solution:
- Option A: \(-5\) (not a solution, since \(-5 < -4\))
- Option B: \(-4\) (is a solution, since \(-4 = -4\))
- Option C: \(0\) (is a solution, since \(0 > -4\))
- Option D: \(5\) (is a solution, since \(5 > -4\))

Thus, the number that is NOT a solution to the inequality is:
**Option A: -5**