Question

Solve the compound inequality.

2x – 2 < –12 or 2x + 3 > 7


x < –7 or x > 5


x < –5 or x > 2


x < –5 or x > 5


x < –12 or x > 2

Answer 1

To solve the compound inequality \( 2x - 2 < -12 \) or \( 2x + 3 > 7 \), we will solve each part separately.

**First inequality:**
\[
2x - 2 < -12
\]
Add 2 to both sides:
\[
2x < -10
\]
Now, divide by 2:
\[
x < -5
\]

**Second inequality:**
\[
2x + 3 > 7
\]
Subtract 3 from both sides:
\[
2x > 4
\]
Now, divide by 2:
\[
x > 2
\]

Now, we combine the results from both inequalities:
\[
x < -5 \quad \text{or} \quad x > 2
\]

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

From the given options, the correct answer is:
**x < -5 or x > 2**.