Tyler Wallace - Beginning and Intermediate Algebra: Learning algebra can be a daunting task. It takes a great teacher like Tyler Wallace to make the whole process less overwhelming

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Special thanks to: My beautiful wife, Nicole Wallace
who spent countless hours typing problems and
my two wonderful kids for their patience and
support during this project
Another thanks goes to the faculty reviewers who reviewed this text: Donna Brown, MichelleSherwood, Ron Wallace, and Barbara Whitney

One last thanks to the student reviewers of the text: Eloisa Butler, Norma Cabanas, IreneChavez, Anna Dahlke, Kelly Diguilio, Camden Eckhart, Brad Evers, Lisa Garza, Nickie Hampshire, Melissa Hanson, Adriana Hernandez, Tiffany Isaacson, Maria Martinez, Brandon Platt,Tim Ries, Lorissa Smith, Nadine Svopa, Cayleen Trautman, and Erin White

Chapter 0: Pre-AlgebraChapter 3: Inequalities0.1 Integers.........................................70.2 Fractions.....................................123.2 Compound Inequalitites............1240.3 Order of Operations....................180.4 Properties of Algebra..................22Chapter 4: Systems of Equations
Chapter 1: Solving Linear Equations1.1 One-Step Equations....................281.2 Two-Step Equations....................331.3 General Linear Equations...........371.4 Solving with Fractions................431.5 Formulas.....................................471.6 Absolute Value Equations...........52Chapter 5: Polynomials1.7 Variation.....................................571.8 Application: Number/Geometry.641.9 Application: Age.........................721.10 Application: Distance................79Chapter 2: Graphing2.1 Points and Lines.........................892.2 Slope...........................................952.3 Slope-Intercept Form................1022.4 Point-Slope Form......................1072.5 Parallel & Perpendicular Lines.112Chapter 6: FactoringChapter 9: Quadratics

Chapter 7: Rational Expressions
7.1 Reduce Rational Expressions....243
Chapter 8: Radicals
8.1 Square Roots.............................288
Chapter 10: Functions
10.1 Function Notation...................386

0.1 Integers ............................................................................................................70.2 Fractions ........................................................................................................120.3 Order of Operations .......................................................................................180.4 Properties of Algebra .....................................................................................220.1 Objective: Add, Subtract, Multiply and Divide Positive and NegativeNumbers.

The ability to work comfortably with negative numbers is essential to success inalgebra. For this reason we will do a quick review of adding, subtracting, multiplying and dividing of integers. Integers are all the positive whole numbers, zero,and their opposites (negatives). As this is intended to be a review of integers, thedescriptions and examples will not be as detailed as a normal lesson.

World View Note: The first set of rules for working with negative numbers waswritten out by the Indian mathematician Brahmagupa.

When adding integers we have two cases to consider. The first is if the signsmatch, both positive or both negative. If the signs match we will add the numbers together and keep the sign. This is illustrated in the following examples

Example 1.5 + (3)

8Same sign,add 5 + 3,keep the negativeOur Solution

Example 2.7 + (5)

12
Same sign,add 7 + 5,keep the negativeOur Solution

If the signs dont match, one positive and one negative number, we will subtractthe numbers (as if they were all positive) and then use the sign from the largernumber. This means if the larger number is positive, the answer is positive. If thelarger number is negative, the answer is negative. This is shown in the followingexamples.

Example 3.7 + 2

5
Different signs,subtract 72,use sign from bigger number,negativeOur Solution

Example 4.

4 + 6
2
Different signs,subtract 64,use sign from bigger number,positiveOur Solution

Example 5.

4 + (3)1Different signs,subtract 43,use sign from bigger number,positiveOur Solution

Example 6.

7 + (10)3Different signs,subtract 107,use sign from bigger number,negativeOur Solution

For subtraction of negatives we will change the problem to an addition problemwhich we can then solve using the above methods. The way we change a subtraction to an addition is to add the opposite of the number after the subtractionsign. Often this method is refered to as add the opposite. This is illustrated inthe following examples.

Example 7.

83
8 + (3)5
Add the opposite of 3
Different signs,subtract 83,use sign from bigger number,positiveOur Solution

Example 8.46

4 + (6)10
Add the opposite of 6
Same sign,add 4 + 6,keep the negativeOur Solution

Example 9.

9(4)9 + 4
13
Add the opposite of4
Same sign,add 9 + 4,keep the positiveOur Solution

Example 10.6(2)

6 + 24Add the opposite of2
Different sign,subtract 62,use sign from bigger number,negativeOur Solution

Multiplication and division of integers both work in a very similar pattern. Theshort description of the process is we multiply and divide like normal, if the signsmatch (both positive or both negative) the answer is positive. If the signs dontmatch (one positive and one negative) then the answer is negative. This is shownin the following examples

Example 11.(4)(6)Signs do not match,answer is negative24Our SolutionExample 12.36Signs match,answer is positive94Our SolutionExample 13.2(6)Signs match,answer is positive12Our SolutionExample 14.15Signs do not match,answer is negative35Our Solution