SOLUTION: What is the largest integer x for which 1/x is larger than 4/49?

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Question 1132165: What is the largest integer x for which 1/x is larger than 4/49?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1%2Fx+%3E4%2F49
1%2A49+%3E4x
49%2F4+%3Ex
or
x%3C49%2F4+

=>the largest integer x for which 1%2Fx is larger than 4%2F49 is highlight%2848%2F4+%29

Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


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.

That technique works well with this problem.

1%2Fx+%3E+4%2F49 --> 4%2F4x+%3E+4%2F49

Since we want 1/x (i.e., 4/4x) to be LARGER than 4/49, we need to have 4x LESS than 49:

4x+%3C+49
x+%3C+49%2F4

The largest integer satisfying that inequality is x=12.