What is the greatest integer value of x such that `1-2x` is at least 6?

Answer

To solve the problem step by step, we need to find the greatest integer value of \( x \) such that \( 1 - 2x \) is at least 6.

### Step 1: Set up the inequality
We start with the inequality given in the problem:
\[ 1 - 2x \geq 6 \]

### Step 2: Isolate the term involving \( x \)
To isolate the term involving \( x \), we subtract 1 from both sides:
\[ 1 - 2x - 1 \geq 6 - 1 \]
This simplifies to:
\[ -2x \geq 5 \]

### Step 3: Solve for \( x \)
Next, we divide both sides of the inequality by -2. Remember that when we divide by a negative number, we must reverse the inequality sign:
\[ x \leq \frac{5}{-2} \]
This simplifies to:
\[ x \leq -2.5 \]

### Step 4: Find the greatest integer value of \( x \)
The greatest integer that is less than or equal to -2.5 is -3. Therefore, we conclude:
\[ \text{Greatest integer value of } x = -3 \]

### Final Answer
The greatest integer value of \( x \) such that \( 1 - 2x \) is at least 6 is:
\[ \boxed{-3} \]