2: Equations and Inequalities

Math 140: College Algebra Workbook with Desmos Applications · LibreTexts

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    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    • 2.1: Linear Expressions and Equations
      This page focuses on solving mathematical problems related to linear equations and rates of change. It provides examples for writing equations based on slopes and points, allowing students to formulate functions under specific conditions. A real-world application discusses municipal solid waste generation, prompting learners to derive equations from historical data for future predictions.
    • 2.2: Linear Equations, Equations In the Plane
      This page focuses on exercises that include graphing equations, determining solutions, and analyzing line relationships. It covers graphing vertical and horizontal lines, identifying parallel and perpendicular lines, and deriving line equations. Students use tools like Desmos to visualize their work, identify solutions for linear equations, and classify relationships between line pairs.
    • 2.3: Solve Linear Inequalities
      This page presents methods for solving inequalities, including double and compound inequalities with examples. It also discusses local zoning regulations concerning the distance properties, specifically a fence around Olive Harvey College, demonstrating a real-world application of these mathematical principles.
    • 2.4: Solving Quadratic Equations
      This page covers solving quadratic equations and determining garden dimensions, emphasizing the use of factored forms to find zeroes of equations and applying equations to express length as a function of width for a garden with an area of \(700 \, \text{ft}^2\). It highlights the importance of algebraic techniques in problem-solving.
    • 2.5: Systems of Equations
      This page offers instructions on solving systems of equations using substitution, elimination, and graphical methods. It provides examples and practice problems with varying coefficients to enhance algebraic skills and understanding. The emphasis is on how different techniques can consistently yield the same solution.
    • 2.6: Introduction to Quadratic Functions
      This page focuses on identifying and analyzing quadratic functions, detailing methods for classification, factoring, finding x-intercepts, and using the quadratic formula. It provides practice examples, including functions in product form and verification through graphical tools like Desmos. The text highlights the importance of reasoning about the graph's characteristics, such as its interaction with the x-axis, and encourages users to confirm algebraic solutions with graphical analysis.

    This page titled 2: Equations and Inequalities was last modified on Fri, 07 Aug 2026 19:06:44 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Lynda Zenati.