Question 1132165
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For some problems involving comparing fractions, a useful technique is to make the NUMERATORS the same; then the larger denominator is the smaller fraction and the smaller denominator is the larger fraction.<br>
That technique works well with this problem.<br>
{{{1/x > 4/49}}} -->  {{{4/4x > 4/49}}}<br>
Since we want 1/x (i.e., 4/4x) to be LARGER than 4/49, we need to have 4x LESS than 49:<br>
{{{4x < 49}}}
{{{x < 49/4}}}<br>
The largest integer satisfying that inequality is x=12.