Question

Solve the compound inequality.
8(3x - 6) < -24 or 2(3b - 2) <4b + 8

Answer 1

To solve the compound inequality \( 8(3x - 6) < -24 \) or \( 2(3b - 2) < 4b + 8 \), we will solve each inequality separately.

### Solving the first inequality:
1. Start with the inequality:
\[
8(3x - 6) < -24
\]

2. Distribute the 8:
\[
24x - 48 < -24
\]

3. Add 48 to both sides:
\[
24x < 24
\]

4. Divide by 24:
\[
x < 1
\]

### Solving the second inequality:
1. Start with the inequality:
\[
2(3b - 2) < 4b + 8
\]

2. Distribute the 2:
\[
6b - 4 < 4b + 8
\]

3. Subtract \( 4b \) from both sides:
\[
2b - 4 < 8
\]

4. Add 4 to both sides:
\[
2b < 12
\]

5. Divide by 2:
\[
b < 6
\]

### Conclusion
The solutions to the compound inequality are:
\[
x < 1 \quad \text{or} \quad b < 6
\]

Thus, the final solution is:
- For \( x \), \( x < 1 \)
- For \( b \), \( b < 6 \)

Therefore, the solution set is:
\[
x < 1 \quad \text{or} \quad b < 6
\]