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4 January, 00:20

What is the greatest integer x for which 7/9 > x/13?

(7/9 and x/13 are both fractions)

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Answers (1)
  1. 4 January, 01:14
    0
    We can solve

    7/9 > x/13

    for x.

    multiply both sides by 13:

    7/9 > x/13

    7/9*13 > x/13 * 3

    7/9*13 > x

    91/9 > x

    reverse it to get

    x < 91/9

    this says that x has to be less than 91/9 for the inequality 7/9 > x/13 to be true.

    91/9 in decimal form is 10.1 repeating.

    the greatest integer x is therefore 10

    answer is 10

    can verify:

    7/9 > x/13

    7/9 is approximately 0.777777 so

    0.7777 > x / 13

    for x = 10, we have 10/13 = 0.7692. and 0.7777 is bigger than that

    try next integer. at x = 11, we have 11/13 = 0.8462. this is bigger than 0.7777

    so the answer is 10. that's the greatest integer
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