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If the student spends x hours on English, then he spends 2x hours on math. The total time he spends on homework is x + 2x = 3x.
Since the student spends no more than 2 hours on homework, we can write the inequality:
3x ≤ 2
To find the maximum time the student can spend on English, we need to solve this inequality for x:
x ≤ 2/3
Therefore, the maximum time the student can spend on English is two-thirds of an hour.