document.write( "Question 1132165: What is the largest integer x for which 1/x is larger than 4/49? \n" ); document.write( "

Algebra.Com's Answer #749106 by greenestamps(13215) $\"\"$ $\"About$

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\n" ); document.write( "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.

\n" ); document.write( "That technique works well with this problem.

\n" ); document.write( " $\"1%2Fx+%3E+4%2F49\"$ --> $\"4%2F4x+%3E+4%2F49\"$

\n" ); document.write( "Since we want 1/x (i.e., 4/4x) to be LARGER than 4/49, we need to have 4x LESS than 49:

\n" ); document.write( " $\"4x+%3C+49\"$
\n" ); document.write( " $\"x+%3C+49%2F4\"$

\n" ); document.write( "The largest integer satisfying that inequality is x=12. \n" ); document.write( "

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