Chapter 3

Verbal Expression

100

All real numbers y greater than or equal to 12

y≥12

200

All real numbers n greater than or equal to -3

n≥−3

300

All real numbers t no greater than 8

t≤8

400

All real numbers p that are less than -2 or greater than 6

p<−2 or p>6

500

All real numbers m that are between –4 and 10, inclusive

−4≤m≤10

Solve & Graph

100

2x+5<11

x<3

200

4y−7≥9

y≥4

300

4(2x−3)+5≤3x+7

x≤14/5 or x≤2.8

400

−2(3y−4)>4y+6

y<1/5

500

(1/2)(6x−4)<2x+1

x<3

Sets

100

List all the subsets of {A, B}.

∅, {A}, {B}, {A, B}

200

How many subsets does the set {cat, dog, fish} have?

2^3=8 subsets

300

List all proper subsets of {1, 3, 5}.

∅, {1}, {3}, {5}, {1, 3}, {1, 5}, {3, 5}

400

If set A = {2, 4, 6, 8} and set B = {4, 8, 10, 12},
what is the intersection of A and B?

A ∩ B = {4, 8}

500

If U = {1, 2, 3, 4, 5, 6, 7, 8},
A = {2, 4, 6, 8}, and
B = {1, 2, 3, 4},
Find (A ∪ B) and (A ∪ B)′ the complement of the union of A and B.

First, find the union:
A ∪ B = {1, 2, 3, 4, 6, 8}

Then, find the complement (elements in U but not in A ∪ B):
(A ∪ B)′ = {5, 7}

Solve & Graph Absolute Values

100

|x−5|=3

x=8 or x=2

200

∣x+4∣>6

x>2 or x<−10

300

2|x−3|+1≤9

−1≤x≤7

400

21|4x−6|+2>x+5

x<0 or x>6

500

|5x−2|+3=2x+10

x=3 or x=−5/7

Compounds

100

2x−3<5x−6<9

1<x<3

200

−4<3x−5<2

1/3<x<7/3

300

−6<2x−8<4

1<x<6

400

−10<4x+2<14

−3<x<3

500

−8<5x−7<12

−1/5 < x < 19/5