What is the greatest integer x for which 7/9 > x/13?
(7/9 and x/13 are both fractions)
1 answer:
We can solve <span>7/9 > x/13 for x. multiply both sides by 13: </span> 7/9 > x/13 7/9*13 > x/13 * 3 <span>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 </span><span>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 </span>
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