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Compound inequality is an inequality made up of two inequalities joined together using 'or' or 'and'.
Given the inequalities 3x > 3 and 9x < 54. Solving both inequalities gives:
3x > 3 and 9x < 54
x > 1 and x < 6
x > 1 is equivalent to x ∈ (1, ∞)
x < 6 is equivalent to x ∈ (-∞, 6)
Therefore, combining the two inequalities together gives:
(1, ∞) ∩ (-∞, 6) = (1, 6)
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