Question

-16\le3x-4<2

Answer 1

To solve the compound inequality \(-16 \leq 3x - 4 < 2\), we can break it into two parts and solve each part separately.

### Step 1: Solve \(-16 \leq 3x - 4\)

1. **Add 4 to both sides**:
\[
-16 + 4 \leq 3x
\]
\[
-12 \leq 3x
\]

2. **Divide by 3**:
\[
-4 \leq x
\]
or
\[
x \geq -4
\]

### Step 2: Solve \(3x - 4 < 2\)

1. **Add 4 to both sides**:
\[
3x - 4 + 4 < 2 + 4
\]
\[
3x < 6
\]

2. **Divide by 3**:
\[
x < 2
\]

### Step 3: Combine the results

Now we combine the results from both parts:
\[
-4 \leq x < 2
\]

### Final Answer

The solution to the compound inequality is:
\[
x \in [-4, 2)
\]