To solve the compound inequality \(-6 \leq 2x - 2 \leq 0\), we can break it into two parts:
- \(-6 \leq 2x - 2\)
- \(2x - 2 \leq 0\)
Step 1: Solve the first inequality \(-6 \leq 2x - 2\)
Add 2 to both sides:
\[ -6 + 2 \leq 2x \]
\[ -4 \leq 2x \]
Now, divide both sides by 2:
\[ -2 \leq x \]
This can also be written as:
\[ x \geq -2 \]
Step 2: Solve the second inequality \(2x - 2 \leq 0\)
Add 2 to both sides:
\[ 2x \leq 2 \]
Now, divide both sides by 2:
\[ x \leq 1 \]
Step 3: Combine the results
From our two inequalities, we have:
\[ -2 \leq x \leq 1 \]
Thus, the solution to the compound inequality \(-6 \leq 2x - 2 \leq 0\) is:
\[ \boxed{[-2, 1]} \]