The sum of 8 consecutive integers is 4. What is the lowest integer?

Options

A. `-3`
B. 0
C. `-2`
D. `-1`

Answer

To solve the problem of finding the lowest integer among 8 consecutive integers whose sum is 4, we can follow these steps:

### Step-by-Step Solution:

1. **Define the First Integer**:
Let the first integer be represented as \( x \).

2. **Express the Consecutive Integers**:
The 8 consecutive integers can be expressed as:
- First integer: \( x \)
- Second integer: \( x + 1 \)
- Third integer: \( x + 2 \)
- Fourth integer: \( x + 3 \)
- Fifth integer: \( x + 4 \)
- Sixth integer: \( x + 5 \)
- Seventh integer: \( x + 6 \)
- Eighth integer: \( x + 7 \)

3. **Set Up the Equation for the Sum**:
The sum of these integers can be written as:
\[ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) + (x + 7) = 4 \]

4. **Simplify the Equation**:
Combine like terms:
\[ 8x + (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7) = 4 \]
The sum of the integers from 0 to 7 is 28, so we can rewrite the equation as:
\[ 8x + 28 = 4 \]

5. **Isolate \( x \)**:
Subtract 28 from both sides:
\[ 8x = 4 - 28 \]
\[ 8x = -24 \]

6. **Solve for \( x \)**:
Divide both sides by 8:
\[ x = \frac{-24}{8} = -3 \]

7. **Identify the Lowest Integer**:
Since \( x \) is the first integer, the lowest integer among the 8 consecutive integers is:
\[ \text{Lowest integer} = x = -3 \]

### Final Answer:
The lowest integer is \( -3 \).

---