Alpha Teach Yourself Algebra I in 24 Hours

Cover Page......Page 1
Title Page......Page 3
Copyright Page......Page 4
Dedication Page......Page 5
Contents......Page 9
Introduction......Page 15
Part One: The Language of Algebra......Page 19
Hour One: Algebraic Expressions......Page 21
Understanding Grouping Symbols......Page 22
Following the Rules for Order of Operations......Page 23
Solving Practical Problems with Algebraic Expressions......Page 24
Answers to Sample Problems in Hour 1......Page 26
Hour’s Up!......Page 27
Plotting Positives, Negatives, and Zero......Page 29
Ordering Rational and Irrational Numbers......Page 31
Finding Absolute Values......Page 34
Answers to Sample Problems in Hour 2......Page 36
Hour’s Up!......Page 37
Adding Real Numbers......Page 39
Subtracting Real Numbers......Page 43
Multiplying Real Numbers......Page 46
Answers to Sample Problems in Hour 3......Page 48
Hour’s Up!......Page 49
Identifying the Properties of Real Numbers......Page 51
Identity Property of Multiplication......Page 52
Using the Properties of Real Numbers......Page 53
Using Multiplication Rules with Real Numbers......Page 56
Using the Division Rule with Real Numbers......Page 58
Answers to Sample Problems in Hour......Page 60
Hour’s Up!......Page 61
Part Two: Solving Equations......Page 63
Solving Equations with Addition and Subtraction......Page 65
Solving Equations with Multiplication or Division......Page 69
Solving Practical Problems with Linear Equations......Page 72
Answers to Sample Problems in Hour 5......Page 74
Hour’s Up!......Page 75
Solving Equations with Combined Operations......Page 77
Solving Equations with the Variable on Both Sides......Page 81
Solving Equations with No Solutions or Many Solutions......Page 84
Solving Practical Problems Using Linear Equations......Page 85
Answers to Sample Problems in Hour 6......Page 87
Hour’s Up!......Page 88
Part Three: All About Polynomials......Page 91
Exponents......Page 93
Following the Order of Operations with Exponents......Page 95
Adding and Subtracting Polynomials......Page 98
Multiplying Exponential Terms......Page 99
Answers to Sample Problems......Page 102
Hour’s Up!......Page 103
Solving Equations That Include Polynomial Terms......Page 105
Solving Word Problems with Basic Polynomial Equations......Page 106
Multiplying Monomials and Polynomials......Page 109
Multiplying Polynomials......Page 110
Multiplying Two Binomials......Page 112
Answers to Sample Problems......Page 114
Hour’s Up!......Page 115
Dividing Monomials......Page 117
Answers to Sample Problems......Page 124
Hour’s Up!......Page 125
Solving Factored Equations......Page 127
Factoring Trinomials......Page 131
Solving Equations by Factoring......Page 135
Answers to Sample Problems......Page 138
Hour’s Up!......Page 139
Part Four: Fundamentals of Fractions......Page 141
Simplifying Algebraic Fractions by Factoring......Page 143
Multiplying Algebraic Fractions Containing Exponents......Page 148
Dividing Algebraic Fractions......Page 150
Answers to Sample Problems......Page 151
Hour’s Up!......Page 152
Adding Algebraic Fractions......Page 155
Subtracting Algebraic Fractions......Page 157
Finding and Using Least Common Denominators......Page 159
Answers to Sample Problems......Page 161
Hour’s Up!......Page 162
Setting Up and Simplifying Ratios to Solve Problems......Page 165
Using Proportions......Page 170
Setting Up and Solving Percent Problems......Page 173
Answers to Sample Problems......Page 178
Hour’s Up!......Page 179
Solving Percent of Increase or Decrease Problems......Page 181
Setting Up and Solving Mixture Problems......Page 185
Setting Up and Solving Work Problems......Page 189
Answers to Sample Problems......Page 192
Hour’s Up!......Page 194
Part Five: Systems of Linear Equations......Page 197
Plotting Ordered Pairs on a Graph......Page 199
Graphing Two-Variable Equations Using the Intercepts......Page 202
Finding the Slope of a Line, Given Two Points......Page 207
Answers to Sample Problems......Page 212
Hour’s Up!......Page 213
Finding the Equation of a Line from the Slope and y-Intercept......Page 219
Finding the Equation of a Line from the Slope and Finding the Equation of a Line......Page 225
Finding the Equation of a Line from Two Points on the Line......Page 227
Solving Direct Variation Problems......Page 229
Solving Inverse Variation Problems......Page 232
Answers to Sample Problems......Page 234
Hour’s Up!......Page 237
Using Graphs to Solve a System of Equations......Page 241
Solving a System of Equations by Substitution......Page 245
Solving a System of Equations by Addition......Page 249
Answers to Sample Problems......Page 254
Hour’s Up!......Page 255
Solving a System of Equations with the Multiplication/Addition Method......Page 259
Solving Practical Problems with Systems of Equations......Page 266
Answers to Sample Problems......Page 272
Hour’s Up!......Page 274
Solving and Graphing Inequalities......Page 277
Solving and Graphing Combined Inequalities......Page 287
Answers to Sample Problems......Page 289
Hour’s Up!......Page 291
Solving and Graphing Absolute Value Equations......Page 293
Solving and Graphing Absolute Value Inequalities......Page 297
Graphing Inequalities with Two Variables......Page 303
Answers to Sample Problems......Page 308
Hour’s Up!......Page 310
Part Six: Quadratic Equations......Page 313
Simplifying Square Roots of Numbers......Page 315
Simplifying Square Roots That Include Variables......Page 323
Solving Equations That Include a Squared Variable......Page 324
Answers to Sample Problems......Page 328
Hour’s Up!......Page 329
Multiplying, Dividing, and Simplifying Square Roots......Page 331
Solving Simple Radical Equations......Page 340
Answers to Sample Problems......Page 345
Hour’s Up!......Page 346
Hour Twenty-three: Quadratic Equations: Solving by Three Methods......Page 349
Solving Quadratic Equations by Finding Square Roots......Page 350
Solving Quadratic Equations by Factoring......Page 353
Solving Quadratic Equations by Completing the Square......Page 357
Answers to Sample Problems......Page 364
Hour’s Up!......Page 365
Solving Quadratic Equations with the Quadratic Formula......Page 367
Choosing the Best Method for Solving Quadratic Equations......Page 375
Finding the Number and Type of Quadratic Equation Solutions......Page 377
Solving Practical Problems with Quadratic Equations......Page 381
Answers to Sample Problems......Page 383
Hour’s Up!......Page 385
Appendix A: Glossary......Page 387
Appendix B: Hour’s Up! Answers......Page 393
Index......Page 403