Question

Suppose b > d +1/3 ,c+1<a – 4, and d + 5/8> a + 2. Order a, b, c, and d from greatest to least. Explain your reasoning.

Answer 1

Let's first write down properties of order used here :

1. $x>y, z>h$ implies $x+z>y+h$
2. $x>y, y>z$ implies $x>z$

Now let's analyze every inequality we have :

• $b>d+\frac{1}{3}$ implies $b>d$ , as $\frac{1}{3}>0$ and thus $b > d+\frac{1}{3} >d$
• $c+1<a-4$ implies $c<a$, as $c+1<a-4$ implies $c<a-5<a$
• $d+\frac{5}{8}>a+2$ implies $d>a$ , as $d+\frac{5}{8} > a+2$ implies $d>a+1 \frac{3}{8}>a$

Thus we have $b>d, d>a, a>c$ so we can conclude that $b>d>a>c$ and the ordering from the greatest to the least is $b,d,a,c$ .