Note that inequalities have many rules similar to equations, and thus we can balance the inequality by subtracting everything by a:

0 < a < b/2 < 9

-a < 0 < b/2 - a < 9 - a

So the answer is A.

If it's not too much trouble, could you explain what you mean by balancing the inequality, and why we subtract everything by a to do that? Thank you!

- He actually simplified the inequality and for each term subtracted a.


\(0 < a < \frac{b}{2} < 9\)

using -a

\(-a < 0 < \frac{b}{2} - a < 9 - a\)

As you can see inside the inequality \(\frac{b}{2} - a < 9 - a\)
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GIVEN: 0 < a < b/2 < 9
Subtract a from all sides to get: 0 - a < a - a < b/2 - a < 9 - a
Simplify: -a < 0 < b/2 - a < 9 - a

If we ignore the first two values, we can see that: b/2 - a < 9 - a
Since 9 - a is GREATER THAN b/2 - a, the correct answer is A

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We can easily eliminate -a from the inequality since it's on both the sides. After that, only 9 and b/2 are left, and 9 is bigger is given in the question.

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Adding +a in both the quantities,
Quantity A = 9
Quantity B= b/2
Given that,
b/2 <9, hence Quantity A > Quantity B

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