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

[xowe]

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}.

 

[HallsofIvy]

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}.

 

[HallsofIvy]

If x= 10, then x+ 3= 10+3= 13. Yes! That's larger than 13.

I meant, of course, "larger than 8".

 

[xowe]

Ah, ha! Thank you, now I get it...xowe

 

[nik4444]

Its been 8 years since this was posted but it still helped me with my 8th grade math THANK YOU