Question

Solve the compound inequality
3x-4<5 or 3x+4>25

Answer 1

To solve the compound inequality \( 3x - 4 < 5 \) or \( 3x + 4 > 25 \), we will solve each part separately.

1. **Solve \( 3x - 4 < 5 \)**:

\[
3x - 4 < 5
\]
Add 4 to both sides:
\[
3x < 9
\]
Divide both sides by 3:
\[
x < 3
\]

2. **Solve \( 3x + 4 > 25 \)**:

\[
3x + 4 > 25
\]
Subtract 4 from both sides:
\[
3x > 21
\]
Divide both sides by 3:
\[
x > 7
\]

Now, we combine the solutions from both parts. The solution to the compound inequality \( 3x - 4 < 5 \) or \( 3x + 4 > 25 \) is:

\[
x < 3 \quad \text{or} \quad x > 7
\]

In interval notation, the solution is:

\[
(-\infty, 3) \cup (7, \infty)
\]