`-1ltxlt3`
The inequality above is equivalent to which of the following?

Options

A. `|x-1|lt2`
B. `|x+1|lt2`
C. `|x-2|lt1`
D. `|x+2|lt1`

Answer

To solve the inequality \(-1 < x < 3\) and express it in terms of absolute value, we can follow these steps:

### Step 1: Understand the inequality
The given inequality states that \(x\) is greater than \(-1\) and less than \(3\). This means that \(x\) lies between these two values on the number line.

### Step 2: Rewrite the inequality
We can rewrite the inequality in a more manageable form. To do this, we can express \(x\) in terms of its distance from a central point.

### Step 3: Identify the center point
The center point between \(-1\) and \(3\) can be calculated as:
\[ \text{Center} = \frac{-1 + 3}{2} = \frac{2}{2} = 1 \]

### Step 4: Calculate the distance from the center
Next, we calculate the distance from the center point \(1\) to the endpoints \(-1\) and \(3\):
- The distance from \(1\) to \(-1\) is \(1 - (-1) = 2\).
- The distance from \(1\) to \(3\) is \(3 - 1 = 2\).

### Step 5: Write the absolute value inequality
Since \(x\) is within \(2\) units of \(1\), we can express this as:
\[ |x - 1| < 2 \]

### Step 6: Conclusion
Thus, the inequality \(-1 < x < 3\) can be rewritten in terms of absolute value as:
\[ |x - 1| < 2 \]