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2: Equations and Inequalities

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    170182

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    An equation states that two expressions are equal, while an inequality relates two different values.

    Source: Boundless. “Equations and Inequalities.” Boundless Algebra. Boundless, 21 Jul. 2015. Retrieved 22 Dec. 2015 from www.boundless.com/algebra/te...ties-63-10904/

    Source: Boundless. “Equations and Inequalities.” Boundless Algebra. Boundless, 21 Jul. 2015. Retrieved 22 Dec. 2015 from www.boundless.com/algebra/te...ties-63-10904/
    An equation states that two expressions are equal, while an inequality relates two different values.

    Source: Boundless. “Equations and Inequalities.” Boundless Algebra. Boundless, 21 Jul. 2015. Retrieved 22 Dec. 2015 from www.boundless.com/algebra/te...ties-63-10904/

    Source: Boundless. “Equations and Inequalities.” Boundless Algebra. Boundless, 21 Jul. 2015. Retrieved 22 Dec. 2015 from www.boundless.com/algebra/te...ties-63-10904     Linear functions are a specific type of function that can be used to model many real-world applications, such as plant growth over time. In this chapter, we will explore linear functions, their graphs, and how to relate them to data.

    • 2.1: The Rectangular Coordinate Systems and Graphs
      Descartes introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Descartes named the horizontal axis the \(x\)-axis and the vertical axis the \(y\)-axis. This system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the \(x\)-axis and the \(y\)-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant.
    • 2.2: Linear Equations
      A linear equation is an equation in which the only exponent applied to the variable(s) is 1. Linear equations in one variable may take the form ax+b=0 and are solved using basic algebraic operations. Linear equations in two variables may be written in the form ax + by = c, and the set of all ordered pair solutions (x,y) will always form a straight line in the Cartesian plane.
    • 2.3: Models and Applications
      A linear equation can be used to solve for an unknown in a number problem. Applications can be written as mathematical problems by identifying known quantities and assigning a variable to unknown quantities.  There are many known formulas that can be used to solve applications. Distance problems are solved using the d = rt formula. Geometry problems are solved using the perimeter formula P = 2L+2W and the area formula A = LW.
    • 2.4: Complex Numbers
      The square root of any negative number can be written as a multiple of i. To plot a complex number, we use two number lines, crossed to form the complex plane. The horizontal axis is the real axis, and the vertical axis is the imaginary axis. Complex numbers can be added and subtracted by combining the real parts and combining the imaginary parts. Complex numbers can be multiplied and divided.
    • 2.5: Quadratic Equations
      Many quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. Another method for solving quadratics is the square root property. The variable is squared. We isolate the squared term and take the square root of both sides of the equation.
    • 2.6: Other Types of Equations
      We can solve radical equations by isolating the radical and raising both sides of the equation to a power that matches the index. In this section we will will also explore the solutions to rational equations in which the variable appears in the denominator. These techniques may produce extraneous solutions, therefore we must check our results to ensure accurate solutions.
    • 2.7: Linear Inequalities and Absolute Value Inequalities
      In this section, we will explore various ways to express sets of numbers using a number line, set builder notation and interval notation. We will use these notations to present the solution sets of inequalities, compound inequalities, absolute value equations and inequalities.
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    Contributors

    This page titled 2: Equations and Inequalities is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Leif Jordan (College of the Desert) via source content that was edited to the style and standards of the LibreTexts platform.