If $$25^{3x} < 125^2$$, what is the greatest possible integer value of $$x$$?

Correct.
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Since $$25 = 5 \cdot 5 = 5^2$$, and $$125 = 5 \cdot 5 \cdot 5 = 5^3$$, then $$25^{3x} < 125^2$$ can be expressed as
>$$(5^2)^{3x} < (5^3)^2$$
>$$5^{6x} < 5^6$$.
Since the bases are the same, ignore the bases and compare the exponents directly.
>$$6x < 6$$
>$$x < 1$$
Hence, the largest possible integer value of $$x$$ is 0.

Incorrect.
While -2 is a possible integer value for $$x$$, it is not the greatest integer value.
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Incorrect.
Note that the question uses an inequality, not an equation. If you've done your calculation right, $$x$$ cannot equal 1.
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Incorrect.
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Incorrect.
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-2

0

1

2

3