If `|10y - 4| > 7 and y < 1`, which of the following could be y?

Options

A. `-0.8`
B. `-0.1`
C. `0.1`
D. `0`

Answer

To solve the inequality \( |10y - 4| > 7 \) and the condition \( y < 1 \), we can break it down into steps.

### Step-by-Step Solution:

1. **Understanding the Absolute Value Inequality**:
The expression \( |10y - 4| > 7 \) means that either:
\[ 10y - 4 > 7 \quad \text{or} \quad 10y - 4 < -7 \]

2. **Solving the First Inequality**:
For the first case, \( 10y - 4 > 7 \):
\[ 10y > 7 + 4 \]
\[ 10y > 11 \]
Dividing both sides by 10:
\[ y > \frac{11}{10} = 1.1 \]

3. **Solving the Second Inequality**:
For the second case, \( 10y - 4 < -7 \):
\[ 10y < -7 + 4 \]
\[ 10y < -3 \]
Dividing both sides by 10:
\[ y < \frac{-3}{10} = -0.3 \]

4. **Combining the Results**:
From the two inequalities, we have:
- \( y > 1.1 \)
- \( y < -0.3 \)

However, we also have the condition \( y < 1 \) given in the problem. Since \( y > 1.1 \) contradicts \( y < 1 \), we discard this case.

5. **Final Conclusion**:
The only valid solution is from the second inequality:
\[ y < -0.3 \]
Therefore, \( y \) must be less than \(-0.3\).