Apabila 3x, 3/x, dan 15/x adalah bilangan bulat, mana yang bisa merupakan bilangan bulat untuk

Summary

This video script explains how to determine the values of x that make the expressions 3x/3 and 15/x integers. The presenter explores different methods, first using the greatest common divisor (GCD) and later testing fractional values of x like 1/3. The key conclusion is that for all integer values of x, specifically when x = 3, both expressions are integers. The presenter dismisses options where x is a fraction, highlighting that option B, where x = 3, is the correct choice. The video encourages viewers to think critically about integer solutions and divisibility.

Takeaways

• 😀 The problem involves determining which values of x make the expressions 3x, 3/x, and 15/x integers for all values of x.
• 😀 The approach starts with determining that the expressions should be divisible by 3 to be integers.
• 😀 The key method used is finding the greatest common divisor (GCD), also referred to as FPB (Faktor Persekutuan Terbesar) in the script.
• 😀 The correct value of x is found by calculating the GCD of 3 and 15, which is 3.
• 😀 After using x = 3, it is verified that 3x, 3/x, and 15/x are all integers.
• 😀 An alternative example with x = 1/3 is considered, showing that not all values of x result in integers for the given expressions.
• 😀 When x = 1/3, the expressions give fractional values, showing that 1/3 does not work for all the options.
• 😀 The correct answer is option 3, which is the only one that satisfies the condition of being an integer for all values of x.
• 😀 The script emphasizes that to get integers for all x, the values of x must be carefully chosen to ensure divisibility.
• 😀 The script concludes by confirming that options 1 and 2 do not work, and only option 3 is valid for all x.

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