A number is greater than 8. The same number is less than 10. The inequalities x greater-than 8 and x less-than 10 represent the situation. Which best explains the number of possible solutions to the inequality? There is one solution because 9 is the only number between 8 and 10. There are a three solutions because 8, 9, and 10 are possible solutions. There are a few solutions because there are some fractions and decimals between 8 and 10. There are infinite solutions because there is always another number between any two numbers.

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02-02-2022
Mathematics

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A number is greater than 8. The same number is less than 10. The inequalities x greater-than 8 and x less-than 10 represent the situation. Which best explains the number of possible solutions to the inequality? There is one solution because 9 is the only number between 8 and 10. There are a three solutions because 8, 9, and 10 are possible solutions. There are a few solutions because there are some fractions and decimals between 8 and 10. There are infinite solutions because there is always another number between any two numbers.

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Answer:

Our inequality is 8 < x < 10, where x is our number.

Since the problem doesn't specify whether the number x is an integer or not, we can assume that x can be either a decimal or a whole number. That means that we want any decimal number or whole number between 8 and 10. The only whole number is 9, but there are infinitely many decimal solutions. For example, we could have 8.001, 8.0001, 8.00001, etc.

Thus the answer is D.

Hope this helps!

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