Finding Solutions with a Replacement Set: x + 3 > 8

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In summary, the conversation is about a person seeking help with a math problem and the expert explains how to find the solution set for the given inequality. The expert provides two ways to solve the problem and concludes that the solution set is {6, 10}. The person expresses their gratitude for the explanation.
  • #1
xowe
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Hey, I'm new and trying to study for school which is starting again soon. I'm not very math smart, and need some help. How would I work out this problem? Thanks...xowe

Find the solution set for x + 3 > 8 if the replacement set is {0, 2, 5, 6, 10}.
 
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  • #2
Since you are given a finite "replacement set" (i.e. possible values for x), the simplest way to do this is just try each value and see what happens:

If x= 0, then x+3= 0+3= 3. No, that's not larger than 8.
If x= 2, then x+3= 2+3= 5. No, that's not larger than 8.
If x= 5, then x+3= 5+3= 8. No, that's not LARGER than 8.
If x= 6, then x+3= 6+3= 9. Yes! That's larger than 8
If x= 10, then x+ 3= 10+3= 13. Yes! That's larger than 13.
The solution set is {6, 10}.

Another way to do this is to solve the inequality generally:
x+ 3> 8- subtract 3 from both sides: x> 5. The only members of the replacement set that are larger than 5 are 6 and 10: the solution set is {6, 10}.
 
  • #3
If x= 10, then x+ 3= 10+3= 13. Yes! That's larger than 13.

I meant, of course, "larger than 8".
 
  • #4
Ah, ha! Thank you, now I get it...xowe
 
  • #5
Its been 8 years since this was posted but it still helped me with my 8th grade math THANK YOU
 

What is a replacement set?

A replacement set is a set of objects that can be substituted for the elements of another set. It is used in set theory to define functions and operations on sets.

What is the purpose of a replacement set?

The purpose of a replacement set is to allow for the substitution of elements in a set, which can be useful in defining functions and operations on sets.

How is a replacement set different from a subset?

A replacement set is different from a subset in that a subset is a set that contains elements from another set, while a replacement set is a set of objects that can be substituted for the elements of another set.

Can a replacement set be empty?

Yes, a replacement set can be empty if there are no objects that can be substituted for the elements of the original set. This would result in the original set remaining unchanged.

What are some examples of using a replacement set?

One example of using a replacement set is in defining a function. For instance, if we have a set of numbers and want to multiply each number by 2, we can use a replacement set of 2 to substitute for each element in the original set. Another example is in set operations, where a replacement set can be used to substitute for elements in the union or intersection of two sets.

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