Im thinking of an integer. Half of this integer is more than one third of the next integer. What is this integer?

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Im thinking of an integer.
Half of this integer is more than one third of the next integer.
What is this integer?
:
x = "the integer"
:
{{{1/2}}}x > {{{1/3}}}(x+1)
multiply by 6, results
3x > 2(x+1)
3x > 2x + 2
3x - 2x > 2
x > 2
:
See if that is true, assume x=3
{{{1/2}}}(3) > {{{1/3}}}(4)
1.5 > 1.33

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