Algebra Chapter 3

Solving Inequalities

100

x/5 < -6

x < -30

200

x - 6 > -3

x > 3

300

4 < 3x - 5 < 7

3 < x < 4

400

6m - 15 < 9 or 10m > 84

m < 4 or m > 8.4

500

3n - 7 > n + 1 or 4n - 5 < 3n - 3

n>4 or n<2

Phrases

100

Twenty-four is less than five eights of a number x

24 < 5/8x

200

Eight less than a number x is at least 17

x - 8 > 17

300

The freezer temperature is to be kept between 15 degrees F and 25 degrees F, inclusive

15 < x < 25

400

At a large nursery, a border for a rectangular garden is being built. Designers want the border’s length to be 5 ft greater than its width. A maximum of 180 ft of fencing is available for the border. Write and solve an inequality that describes possible widths of the garden.

2(w + 5) + 2(w) < 180

w < 42.5 ft

500

Is each number a solution of -7x < -21? Solve for each value.

a. 3

b. 0

c. 8/3

d. 4

a. -21 < -21, NO

b. 0<-21, NO

c. -18.66 < -21, NO

d. -28 < -21, YES

Interval Notation

100

(-infinity, 5)

x < 5

200

[2,9)

2 < x < 9

300

(-infinity,1) or [6,infinity)

x < 1 or x > 6

400

10 < x < 18

(10,18]

500

x < -6 or x > 5

(-infinity, -6)or(5,infinity)

Unions and Intersections

100

Let X = {1,4,9} let Y = {x|x is an odd whole number less than 10.

X U Y

X U Y = {1, 3, 4, 5, 7, 9}

200

Let x = {1,4,9} let y = {x|x is an odd whole number less than 10.

X n Y

X n Y = {1, 9}

300

Let x = {1,4,9} let y = {x|x is an odd whole number less than 10 and Z = {2,4,6,8}

X U Z

X U Z = {1,2,4,6,8,9}

400

Let x = {1,4,9} let y = {x|x is an odd whole number less than 10 and Z = {2,4,6,8}

Y n Z

Y n Z = {}

500

Let x = {1,4,9} let y = {x|x is an odd whole number less than 10 and Z = {2,4,6,8}

Y U Z

Y U Z = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Absolute Value

100

|x| = 5

x = 5 or -5

200

|a + 2|>4

a > 2 or a < -6

300

|8 - w| < 8

0 < w < 16

400

|3c| - 1 > 11

c > 4 or c < -4

500

|t| - 5 < 3

-8 < t < 8