• The sections in the Worktext do NOT follow a mathematical decimal pattern.  They follow a chapter - section pattern.  So, 1.12 means "chapter 1, section 12" and comes after 1.11.  In other words the order is 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, and so on.
• The Worktext Section below is linked to a website with explanations and exercises.  You will want to explore the options on this site to both see what is available and to help you learn.

....An important idea is "order of operations" 

• This is a site I have written.
• This one is from math.com.  I like that it includes explanations and examples for you to work.  However, it does have annoying banners.
• And another one from purplemath.

...Another basic concept is "using the distributive property and combining like terms"

• This is a site I have written.
• Purple Math at http://www.purplemath.com/modules/polyadd.htm gives additional explanations.
• Ask Dr. Math at http://mathforum.org/library/drmath/view/56380.html gives another explanation.

• For a more complete explanation with sample problems go to http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=polyadd.

..This site will help you understand the relationship among sets of numbers

• This is a site I have written.

..An important skill set is the ability to solve linear equations

• This is a site I have written.
• Purple Math at http://www.purplemath.com/modules/solvelin.htm gives additional explanations.
• For a more complete explanation with sample problems go to http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=solveq

..To help you solve inequalities

• This is a site I have written.

Beginning Algebra

119 Objectives

Sample Problem

Worktext Section

I. Real Numbers

A. Operations, substitution and evaluation

alge005: Evaluation of a linear expression in two variables

Evaluate the expression
x –  3c when x = 2 and c = – 6.

1.3

alge004: Evaluation of a polynomial in one variable

Evaluate the expression when c = – 2

1.4

B. Algebraic symbols

alge015: Writing an inequality

Write the algebraic expression for the sentence
" 3 is greater than a.”

1.6

alge016: Translating sentences into linear equations

Write the algebraic expression for the sentence
" 3 plus a equals 2."

1.5

alge186: Writing a compound inequality

Write " x is greater than or equal to – 6 and less than – 4" as an algebraic expression.

1.7

alge602: Writing a mathematical expression

Write an algebraic expression to answer the question below.
How many minutes are there in h hours?
Answer:  60h minutes

C. Number system

alge001: Integer and rational numbers

For each of the two number systems, indicate all the numbers which belong to it. (Problems in ALEKS)

1.1

alge002: Integer, rational and irrational numbers (real)

For each of the four number systems, indicate all the numbers which belong to it.
(Problems in ALEKS)

1.2

D. Properties of real numbers

alge606: Distributive Property, simple

Use the Distributive Property to remove the parentheses from the following expression:
(u – 12)(5)
Answer: 5u – 60

1.9

alge604: Distributive Property, advanced

Use the Distributive Property to remove the parentheses from the following expression:
(4 – 3y + 4t)(-7))
Answer: – 28 + 21y  – 28t

1.9

alge607: Combining like terms, basic

Simplify the following expression:
-12w + 3 w
Answer: - 9w

1.9

alge187: Properties of addition

For each equation below, indicate the property that justifies the equation by filling in the box with the appropriate number.

   6 + (b + 4) = (6 + b) + 4     [   ]
   0 = (-3) + 3                         [   ]
   5 + 0 = 5                            [   ]

Answer:

   6 + (b + 4) = (6 + b) + 4     [ 2 ]
   0 = (-3) + 3                         [ 4 ]
   5 + 0 = 5                            [ 3 ]

1.9

alge188: Properties of real numbers

For each equation below, indicate the property that justifies the equation by filling in the box with the appropriate number

  9 + 3 = 3 + 9                 [   ]

                         [   ]

   5 + 0 = 5                      [   ]

           [   ]

Answer:

  9 + 3 = 3 + 9                 [ 1 ]

                         [ 9 ]

   5 + 0 = 5                      [ 3 ]

           [ 7 ]

1.9

II. Solving Linear Equations

A. One occurrence of the variable

alge010: Additive property of equality: Problem type 2

What is the value of  w if
w + 2 = – 9?

2.2

alge226: Additive property of equality: Problem type 3

If 153 = 242 –  w,
what is the value of w?

2.3

alge802:Multiplicative property of equality with fractions

alge008:Multiplicative property of equality: Problem type 1

Solve for w: 3w = 87

2.4

alge012: Multiplicative property of equality: Problem type 2

Solve the following equation for t:  

2.5

alge006: Solving a linear equation: Problem type 1

Solve the following equation for t:
 2t – 3 = 5

2.6

alge208: Solving a linear equation: Problem type 2

Solve for x:  

2.7

alge200: Solving a linear equation: Problem type 3

Evaluate the expression
2x + 10, given that 11x – 2 = 9.

2.8

B. Several occurrences of the variable

alge011: Solving a linear equation with several occurrences of the variable: Problem type 1 

What is the value of u if 
2(u– 4) – 5u = – 29

2.9

alge061: Solving a linear equation with several occurrences of the variable: Problem type 2 

Solve for x:  Write your answer as a fraction in simplest form.

Answer:

2.10

alge013: Solving a linear equation with several occurrences of the variable: Problem type 3

Solve the following equation for x :

2.11

alge209: Solving a linear equation with several occurrences of the variable: Problem type 4

Solve the following equation for x:

2.12

alge179: Solving a linear equation with several occurrences of the variable: Problem type 5

Solve for u:

2.13

The surface area S of a right prism is given by

S = 2 B + Ph,
where B is the area of the base, P is the perimeter, and h is the height of the prism. Solve for P.

5.17

C. Inequalities

alge019: Solving a linear inequality: Problem type 1

Solve the inequality t – 5 <  20 for t

2.16

alge020: Solving a linear inequality: Problem type 2

Solve the inequality
11x – 2 > 9 for x.

2.17

alge021: Solving a linear inequality: Problem type 3

Solve the inequality
– 4z – 19 < – 3 for z.

2.18

alge207: Solving a linear inequality: Problem type 4

Solve the inequality  for w.

2.19

alge017: Graphing a linear inequality on the number line

2.20

alge166: Graphing a compound linear inequality on the number line

Graph the portion of the number line containing all points for which
x < – 6 or x > 9

2.21

D. Applications

alge014: Solving a word problem using a linear equation: Problem type 1

A total of 328 tickets were sold for the school play. The number of student tickets sold is three times the number of adult tickets sold. How many student tickets were sold?
Answer:
Let S = number of student tickets sold, and
 and A = number of adult tickets sold.
Since the number of student tickets sold is three times the number of adult tickets sold S=3A.
Since, S = 3A and S + A = 328,
3A + A = 328.
Solving for A we have, A = 82.
S = 3A = 246 tickets.
There were 246 adult tickets sold.

2.14

alge219: Solving a word problem using a linear equation: Problem type 2

2.15

Two discounted bouquets of flowers were sold for $43.34. If the discount on each bouquet of flowers was $9.28, what was the price of each bouquet of flowers before discount? (Suppose that each bouquet of flowers has the same price).

2.29

alge704: Solving a word problem using a linear equation: Problem type 4

alge022: Word problem with linear inequalities

The sum of two numbers is less than 12. The second number is 6 more than the first. What are the possible values for the first of the two numbers?
In your answer, denote the first number by x.
Answer:
Let x = the first number
   x + 6 = second number
  x +  x + 6 < 12
  2x  + 6 < 12
  2x < 12
  x < 6

2.22

mstat014: Random samples and prediction

In a magazine survey, 150 randomly selected students from several middle schools throughout the United States are asked whether they have access to a computer at home and if they have a personal e-mail account. The responses of the students are summarized in the following table:

(a)  What percentage of the students surveyed have an e-mail account?
(b)  Answer: 57/150 = 0.38 = 38%

What percentage of the students surveyed have no computer access at home?
Answer: 84/150 = 0.56 = 56%

geom078: Sides of polygons having the same perimeter

Afterward, the wire is bent into an equilateral triangle. Thus, the perimeter of the equilateral triangle is also 48cm.
That is, if S is the length of a side of the equilateral triangle, we have
3S = 48
S = 16 cm