Answer:
c. 5|x
Step-by-step explanation:
The notation "5 | 2x" means that 5 divides 2x, or in other words, 2x is divisible by 5.
Since 2 is a prime number and does not have 5 as a factor, we can conclude that 5 must divide x in order for 5 to divide 2x. Therefore, the statement "5|x" is true.
If 5 divides 2x, this implies that x must also be a multiple of 5, hence, the correct answer is '5|x'. This is because 2 is not divisible by 5, so x must contain the factor 5 for the product 2x to be divisible by 5.
So the correct option is option C
The question involves understanding the divisibility rules for integers, particularly the multiples of 5. The assertion 5 | 2x means that 2x is divisible by 5. This implies that x must contain the factor 5 for 2x to be divisible by 5 since 2 is not divisible by 5.
Therefore, the correct answer is c. 5|x, which states that x is divisible by 5. Please note that 5|2 is incorrect because 2 is not divisible by 5.
To further explain, if 5 divides 2x (5|2x), then there exists an integer k such that 2x = 5k. Since 2 is not a multiple of 5, x must be a multiple of 5 for the equation to hold true. This simplifies to x = (5k/2), and since k is an integer and 2 and 5 have no common factors, the only way for x to be an integer is if k contains the factor 2, making x a multiple of 5. Thus, we conclude that 5|x.
