-6<4х-1<=0

To solve the compound inequality \(-6 < 4x - 1 \leq 0\), we will break it down into two parts and solve each part separately.

Step 1: Solve the first part

\[ -6 < 4x - 1 \]

Add 1 to both sides: \[ -6 + 1 < 4x \] \[ -5 < 4x \]

Now, divide by 4: \[ -\frac{5}{4} < x \] or \[ x > -\frac{5}{4} \]

Step 2: Solve the second part

\[ 4x - 1 \leq 0 \]

Add 1 to both sides: \[ 4x \leq 1 \]

Now, divide by 4: \[ x \leq \frac{1}{4} \]

Step 3: Combine the results

Now we combine the two parts: \[ -\frac{5}{4} < x \leq \frac{1}{4} \]

Final Solution

The solution to the inequality is: \[ -\frac{5}{4} < x \leq \frac{1}{4} \]

In interval notation, this is expressed as: \[ \left(-\frac{5}{4}, \frac{1}{4}\right] \]