Solve `|5 - 4x| lt -2`

Answer

To solve the inequality \( |5 - 4x| < -2 \), we need to analyze the properties of absolute values.

### Step-by-Step Solution:

1. **Understanding Absolute Value**:
The absolute value of any expression, such as \( |5 - 4x| \), is defined as the distance from zero. Therefore, it is always non-negative. This means:
\[ |5 - 4x| \geq 0 \]

2. **Analyzing the Inequality**:
The inequality we have is:
\[ |5 - 4x| < -2 \]
Since the left side \( |5 - 4x| \) is always greater than or equal to zero, it can never be less than \(-2\).

3. **Conclusion**:
Since there are no values of \( x \) that can satisfy the inequality \( |5 - 4x| < -2 \), we conclude that:
\[ \text{No solution} \]

### Final Answer:
There are no values of \( x \) that satisfy the inequality \( |5 - 4x| < -2 \).

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