Appendix A - A.3 - Inequalities - Exercises - Page 545: 8

(a) $a = b$ (b) $a \lt b$

We can state the Trichotomy Property: For any two real numbers $a$ and $b$, exactly one of these statements is true: $a\gt b, ~~a = b, ~~a \lt b$ (a) $a = \frac{12+(-3)}{9} = \frac{9}{9} = 1$ $b = \frac{5^2-4^2}{3^2} = \frac{9}{9} = 1$ $a = b$ (b) $a = 2 \cdot 3 + 4 = 6+4 = 10$ $b = 2 \cdot (3+4) = 2 \cdot (7) = 14$ $a \lt b$