To solve the compound inequality \( 3 < x + 3 < 6 \), we can break it into two parts and solve each part separately:
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Solve \( 3 < x + 3 \): \[ 3 - 3 < x \implies 0 < x \implies x > 0 \]
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Solve \( x + 3 < 6 \): \[ x < 6 - 3 \implies x < 3 \]
Now we can combine the results from the two parts: \[ 0 < x < 3 \]
Thus, the solution for \( x \) is \( 0 < x < 3 \).
Looking at the answer choices:
- a: \( 6 < x < 9 \)
- b: \( 6 > x > 9 \)
- c: \( 0 < x < 3 \) (this is correct)
- d: \( 0 > x > 3 \)
The correct answer is c: \( 0 < x < 3 \).