Answer :

The infinite string of 9s indicates that you are getting infinitely close to the next whole number, which in this case is 7. The correct option is 3, X=7.

In mathematics, when you have a repeating decimal like 6.99999..., it can be interpreted as a limit. This means we consider what value the number approaches as the string of 9s continues indefinitely.

To illustrate this, let's take a simple mathematical approach to explain why x = 7. Consider the fraction [tex]\( \frac{1}{3} \)[/tex]; when written as a decimal, [tex]\( \frac{1}{3} = 0.3333\ldots \)[/tex] (with an infinite string of 3s). If we multiply both sides of this equality by 3 we get:
[tex]\[ 3 \times \frac{1}{3} = 3 \times 0.3333\ldots \][/tex]
[tex]\[ 1 = 0.9999\ldots \][/tex]

From this result, we see that the decimal [tex]\( 0.9999\ldots \)[/tex] (with an infinite string of 9s) is equal to 1. Similarly, if you have [tex]\( 6.9999\ldots \)[/tex], you can think of it as [tex]\( 6 + 0.9999\ldots \).[/tex] Given what we just discovered, that [tex]\( 0.9999\ldots = 1 \)[/tex], then by adding 6 to both sides we have:
[tex]\[ 6 + 0.9999\ldots = 6 + 1 \][/tex]
[tex]\[ 6.9999\ldots = 7 \][/tex]

Therefore, the number [tex]\( x = 6.99999\ldots \)[/tex] is, in fact, equal to 7. The infinite string of 9s indicates that you are getting infinitely close to the next whole number, which in this case is 7. So, answering the question: x = 7. The correct option is: 3, x = 7.

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Rewritten by : Barada