Algebra Know-It-ALL

6. In terms of an inequality statement and set notation, describe how the rational numbers
   relate to the irrational numbers. Here’s a hint: Use the same approach as we did in the
   final challenge.


7. Write the following statement as a “mathematical verse.” Does it represent a valid
   mathematical law? If not, show a counterexample.
   (∀a,b,c) : [(a≥b) & (b≤c)]⇒ (a=c)


8. For what real-number values of x is this equation true?

x+ 4 = 2 x

9. For what real-number values of y is this inequality true?

y/2 ≠ 4 y+ 7

10. For what real-number values of z is this inequality true?

z/(−3)≤ 6 z+ 6

Practice Exercises 191