bunch of questios\ns

1. Solve each inequality. Try to solve some using algebra and others using graphing on a number line.
Express each result using interval notation.
(a) x + 5
3
> 2
(b) −2x − 1 ≤ −9
(c) x
2 ≤ 9
2. If a > b > c > d, then which is larger, a + c or b + d? Can we tell from a > b > c > d which of a + d and
b + c is larger? (Problem 9.25 in the textbook, page 283)
If you are stuck, Problems 9.1 and 9.2 in the textbook may help.
3. Back in elementary school, I learned a great magic trick to compare two positive fractions. Here’s
my magic trick in action. Consider the fractions 5
19 and 6
23 . I multiply the numerator of the first and
the denominator of the second, and get 5 · 23 = 115. I multiply the numerator of the second and the
denominator of the first, and get 6 · 19 = 114. Because 115 > 114, I know that 5
19 >
6
23 .
Why does this magic trick work? In other words, if a, b, c, and d are positive, then why does ad > bc
mean that a
b
>
c
d
? (Problem 9.28 in the textbook, page 283)
If you are stuck, Problem 9.3 in the textbook may help.
4. Which number is bigger, −
1227
1229 or −
1229
1231? Do not use a calculator.