Question

Solve the compound inequality. Graph your solution.

2x – 2 < –12 or 2x + 3 > 7


x < –5 or x > 5


x < –7 or x > 5


x < –5 or x > 2


x < –12 or x > 2

Answer 1

Let's solve the compound inequality step by step.

1. **Solve the first part of the inequality:**
\(2x - 2 < -12\)

Add 2 to both sides:
\[
2x < -10
\]

Now, divide by 2:
\[
x < -5
\]

2. **Solve the second part of the inequality:**
\(2x + 3 > 7\)

Subtract 3 from both sides:
\[
2x > 4
\]

Now, divide by 2:
\[
x > 2
\]

3. **Combine the results:**
From the inequalities we have found:
\[
x < -5 \quad \text{or} \quad x > 2
\]

Thus, the solution to the compound inequality is:
\[
x < -5 \quad \text{or} \quad x > 2
\]

### Graphing the solution:

On the number line:
- For \(x < -5\), draw an open circle at -5 and shade to the left.
- For \(x > 2\), draw an open circle at 2 and shade to the right.

### Final answer:
The correct option from your provided choices is:
**\(x < -5 \quad \text{or} \quad x > 2\)**