Solve: `-2le6x-1lt2`.

Answer

To solve the inequality \(-2 \leq 6x - 1 < 2\), we will break it down step by step.

### Step 1: Break the compound inequality
We start with the compound inequality:
\[ -2 \leq 6x - 1 < 2 \]

### Step 2: Add 1 to all parts of the inequality
To isolate the term with \(x\), we add 1 to all parts of the inequality:
\[ -2 + 1 \leq 6x - 1 + 1 < 2 + 1 \]
This simplifies to:
\[ -1 \leq 6x < 3 \]

### Step 3: Divide all parts by 6
Next, we divide all parts of the inequality by 6 to solve for \(x\):
\[ \frac{-1}{6} \leq x < \frac{3}{6} \]
This simplifies to:
\[ \frac{-1}{6} \leq x < \frac{1}{2} \]

### Step 4: Write the solution set
The solution set can be expressed in interval notation. Since \(-\frac{1}{6}\) is included (due to the "less than or equal to" sign) and \(\frac{1}{2}\) is not included (due to the "less than" sign), we write:
\[ x \in \left[-\frac{1}{6}, \frac{1}{2}\right) \]

### Final Answer
The solution set is:
\[ \left[-\frac{1}{6}, \frac{1}{2}\right) \]

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