https://file.aiquickdraw.com/mathbot/file/1726701890621hfjnnszt.jpg

The problem in the image asks: "What are the solutions of \(-\frac{9}{8}a + 1 < 6\)?" with multiple choices provided for the possible solution ranges of \(a\).

### Let's solve this inequality:

1. Start with the inequality:
   \[
   -\frac{9}{8}a + 1 < 6
   \]
   
2. Subtract 1 from both sides to isolate the term with \(a\):
   \[
   -\frac{9}{8}a < 5
   \]

3. Multiply both sides of the inequality by \(-\frac{8}{9}\) to solve for \(a\), remembering to reverse the inequality sign when multiplying by a negative number:
   \[
   a > -\frac{8 \times 5}{9} = -\frac{40}{9}
   \]

Thus, the solution is:
\[
a > -\frac{40}{9} \quad \text{or approximately} \quad a > -4.44
\]

### Looking at the answer choices:
- The correct inequality is closest to **H. \( a > -63 \)**, though it seems the answer choices are off by magnitude.

Would you like a detailed explanation of the steps, or do you have any other questions?

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### Related Questions:
1. How do you solve inequalities involving fractions and variables?
2. Why does multiplying an inequality by a negative number reverse the inequality sign?
3. What are the differences between solving equalities and inequalities?
4. Can you explain how to check solutions of inequalities by substitution?
5. How can inequalities be represented on a number line?

**Tip**: When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number!

Learn how to solve the inequality -9/8a + 1 < 6 by isolating the variable and applying rules for inequalities with fractions. This problem demonstrates key algebraic concepts, including inequality manipulation and reversing inequality signs when multiplying by a negative number. Suitable for students in Grades 8-10.

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