Question

-6 /leq 2x - 2 /leq 0

Answer 1

To solve the compound inequality \(-6 \leq 2x - 2 \leq 0\), we can break it into two parts:

1. \(-6 \leq 2x - 2\)
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:

\[
\boxed{[-2, 1]}
\]