**Solve for \[b\].**
*Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.*

\[-67b+6 \leq 9b + 43\]

Let's solve the inequality \(-67b + 6 \leq 9b + 43\).

1. **Subtract \(9b\) from both sides**:
   \[
   -67b - 9b + 6 \leq 43
   \]
   Simplifying this gives:
   \[
   -76b + 6 \leq 43
   \]

2. **Subtract 6 from both sides**:
   \[
   -76b + 6 - 6 \leq 43 - 6
   \]
   Simplifying this gives:
   \[
   -76b \leq 37
   \]

3. **Divide both sides by \(-76\)**. Remember, dividing by a negative number reverses the inequality sign:
   \[
   b \geq \frac{37}{-76}
   \]
   Simplifying the fraction to its lowest terms gives:
   \[
   b \geq \frac{-37}{76}
   \]

So, the solution is:
\[
b \geq \frac{-37}{76}
\]

Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. How do you solve inequalities with variables on both sides?
2. What happens when you multiply or divide an inequality by a negative number?
3. How can you check if a solution to an inequality is correct?
4. Can you graph the solution of an inequality on a number line?
5. How do you solve inequalities that involve fractions or decimals?

**Tip:** Always remember to reverse the inequality sign when dividing or multiplying by a negative number!

Learn how to solve the inequality -67b + 6 ≤ 9b + 43 with a detailed step-by-step solution. This problem involves solving inequalities and understanding the principles of inequality manipulation. Suitable for students in Grades 9-12.

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