MTH 60: Algebra 1
- Page ID
- 182287
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This course develops core algebra skills, beginning with number sense and operations with variables, then advancing to solving equations and inequalities, interpreting and creating graphs, and working with systems of equations. Emphasis is placed on understanding relationships between quantities, modeling real-world situations, and applying logical, step-by-step problem-solving strategies.
- Preface
- In this preface, you’ll find a welcome message to set the stage for your learning, guidance on how to use the book effectively, acknowledgments of those who contributed to its creation, and a table of contents to help you navigate the material. This section will help you get oriented and ready to make the most of the resources ahead.
- Unit 1: Introducing Unknowns
- In this unit, we’ll begin our journey into algebra by learning how to work with unknown values and build expressions using variables. We’ll strengthen our number sense as we review operations with integers and fractions, explore the order of operations, and simplify expressions. Along the way, we’ll apply our skills to real-life problems using unit conversions and basic geometry. These foundational tools will help us think algebraically and prepare us for more complex ideas ahead.
- Unit 2: Relating Unknowns
- Now that we’ve learned how to write and simplify expressions, we’ll shift our focus to solving equations and inequalities. We’ll explore techniques for isolating variables, including working with fractions, decimals, and multi-step problems. We’ll also learn how to rearrange formulas and apply our algebra skills to everyday situations like budgeting and travel. By building these connections, we’ll deepen our understanding of how quantities relate to one another.
- Unit 3: Graphing Relationships
- In this unit, we’ll bring algebra to life by visualizing relationships on the coordinate plane. We’ll graph equations and inequalities, explore slope as a rate of change, and write equations to model patterns we see in real-world data. We’ll also interpret graphs to make predictions and decisions. Through these activities, we’ll connect algebraic thinking with geometry and strengthen our ability to communicate mathematical ideas visually.
- Unit 4: Working with Systems
- In this unit, we focus on solving systems of linear equations using graphical and algebraic methods, including substitution and elimination. We also extend these ideas to systems of linear inequalities and interpret their solutions. These tools allow us to analyze multiple constraints and apply algebraic reasoning to real-world situations involving comparisons, choices, and optimization.
- Unit 5: Practice Problem Answers
- This unit provides the answers to all the practice problems from the textbook. It’s here to help you confirm whether your solutions are correct and to support your learning by giving you immediate feedback. However, remember that knowing the final answer is only part of doing math. You’re still responsible for showing clear, step-by-step work that demonstrates your thinking and understanding.