Solve: `-2le6x-1lt2`.

Answer

To solve the inequality \(-2 \leq 6x - 1 < 2\), we will break it down into two parts and solve each part step by step.

### Step 1: Split the Inequality
We can rewrite the compound inequality as two separate inequalities:
1. \(-2 \leq 6x - 1\)
2. \(6x - 1 < 2\)

### Step 2: Solve the First Inequality
Starting with the first inequality:
\[ -2 \leq 6x - 1 \]
Add 1 to both sides:
\[ -2 + 1 \leq 6x \]
This simplifies to:
\[ -1 \leq 6x \]
Now, divide both sides by 6:
\[ -\frac{1}{6} \leq x \]
This can be rewritten as:
\[ x \geq -\frac{1}{6} \]

### Step 3: Solve the Second Inequality
Now, we solve the second inequality:
\[ 6x - 1 < 2 \]
Add 1 to both sides:
\[ 6x < 2 + 1 \]
This simplifies to:
\[ 6x < 3 \]
Now, divide both sides by 6:
\[ x < \frac{3}{6} \]
This simplifies to:
\[ x < \frac{1}{2} \]

### Step 4: Combine the Results
Now we combine the results from both inequalities:
\[ -\frac{1}{6} \leq x < \frac{1}{2} \]

### Final Answer
In interval notation, the solution can be expressed as:
\[ x \in \left[-\frac{1}{6}, \frac{1}{2}\right) \]