Solve the compound inequality 6b < 42 or 4b + 12 > 8.

b < 6 or b > 5
b < 7 or b > −1
b < 7 or b > 1
b > 6 or b < 5

Let's solve the compound inequality step by step.

The given compound inequality is:

\[ 6b < 42 \quad \text{or} \quad 4b + 12 > 8 \]

### Solving the first inequality:
\[
6b < 42
\]
Divide both sides by 6:
\[
b < \frac{42}{6}
\]
\[
b < 7
\]

### Solving the second inequality:
\[
4b + 12 > 8
\]
Subtract 12 from both sides:
\[
4b > 8 - 12
\]
\[
4b > -4
\]
Divide both sides by 4:
\[
b > \frac{-4}{4}
\]
\[
b > -1
\]

### Final solution:
The compound inequality is \( b < 7 \) or \( b > -1 \).

This matches the option:
\[
\boxed{b < 7 \text{ or } b > -1}
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. Solve the inequality: \(3x + 2 < 11\) or \(x - 4 > 0\).
2. Solve the compound inequality: \(5c - 1 > 9\) and \(2c + 3 \leq 11\).
3. What is the solution to \(2d + 8 \leq 4d - 2\)?
4. Solve the inequality \(x/3 - 1 \geq 2\).
5. Find the solution for \(7y - 5 > 2y + 10\).

**Tip:** When solving compound inequalities, always treat each part separately and combine the solutions carefully using "and" or "or."

Solve the compound inequality 6b < 42 or 4b + 12 > 8.
b < 6 or b > 5
b < 7 or b > −1
b < 7 or b > 1
b > 6 or b < 5

Learn how to solve the compound inequality 6b < 42 or 4b + 12 > 8 with a detailed step-by-step solution. This problem explores key algebraic concepts, such as solving linear inequalities and applying compound inequality rules, making it ideal for students in Grades 7-9.

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