-6<4х-1<-0

To solve the double inequality \(-6 < 4x - 1 < -0\), we can break it down into two parts and solve for \(x\).

1. First, solve the left part of the inequality:

\[ -6 < 4x - 1 \]

Add 1 to both sides:

\[ -6 + 1 < 4x \]

\[ -5 < 4x \]

Now, divide by 4:

\[ -\frac{5}{4} < x \]

2. Now, solve the right part of the inequality:

\[ 4x - 1 < 0 \]

Add 1 to both sides:

\[ 4x < 1 \]

Now, divide by 4:

\[ x < \frac{1}{4} \]

3. Combining these results, we have:

\[ -\frac{5}{4} < x < \frac{1}{4} \]

Thus, the solution to the inequality \(-6 < 4x - 1 < 0\) is:

\[ x \in \left(-\frac{5}{4}, \frac{1}{4}\right) \]