In the inequalilty `37 le -2x+1` what is the appropriate order of steps needed to solve the inequality for x?

Options

A. Add 1 to both sides, divide both sides by 2, and flip the inequality sign to `ge`.
B. Subtract 1 from both sides, divide both sides by -2 and flip the inequality sign to `ge`.
C. Add 1 to both sides, divide both sides by -2, and keep the original inequality sign.
D. Subtract 1 from both sides, divide both sides by 2, and keep the original inequality sign.

Answer

To solve the inequality \( 37 \leq -2x + 1 \) for \( x \), we can follow these steps:

### Step 1: Subtract 1 from both sides
We start by isolating the term with \( x \). We can do this by subtracting 1 from both sides of the inequality.

\[ 37 - 1 \leq -2x + 1 - 1 \]

This simplifies to:

\[ 36 \leq -2x \]

### Step 2: Divide both sides by -2
Next, we need to isolate \( x \). To do this, we divide both sides of the inequality by -2. However, remember that when we divide or multiply both sides of an inequality by a negative number, we must flip the inequality sign.

\[ \frac{36}{-2} \geq x \]

This simplifies to:

\[ -18 \geq x \]

### Step 3: Rewrite the inequality
We can rewrite the inequality for clarity:

\[ x \leq -18 \]

### Final Result
Thus, the solution to the inequality \( 37 \leq -2x + 1 \) is:

\[ x \leq -18 \]