Mastering Linear Equations and Inequalities: Essential Techniques Class Lectures

Linear equations and inequalities are fundamental concepts in Algebra 2 that form the basis of many STEM applications. These equations and inequalities are used to model real-world phenomena such as population growth, economic trends, and physical systems. The input of these equations is typically a set of variables representing different aspects of the system being modeled, while the output is a solution that describes the behavior of the system over time. Linear equations and inequalities are also used in STEM fields such as engineering, physics, and computer science to solve complex problems and make predictions about the behavior of systems. Understanding these concepts is essential for success in STEM careers and for developing critical thinking skills.

11 topics

20 Hours

Educators

Course Curriculum

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Matrices and Determinants

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Mastering Quadratic Equations: Essential Tips and Tricks

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Mastering Quadratic Functions: Unlocking Their Power

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Applications of Trigonometric Functions

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Graphing Trigonometry Functions

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Mastering Linear Equations and Inequalities: Essential Techniques Lecture Videos, Solved Step-by-Step

Mastering Linear Equations and Inequalities: Essential Techniques

Absolute Value Functions - Example 3

In mathematics, the absolute value or modulus |x| of a real number "x" is the non-negative value of "x" without regard to its sign. That is, if "x" > 0, then |x| = x; if "x" = 0, then |x| = 0; and if "x" < 0, then |x| = ?x. The absolute value of a real number is also known as its magnitude. The absolute value of a complex number z = x + iy is x^2 + y^2, where x^2 + y^2 = |x + iy| = x^2 + y^2 = |z|.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Correlationand Best- Fitting Lines - Example 4

In statistics, correlation and covariance are two measures of the statistical relationship between two random variables. Correlation is a measure of the strength and direction of the linear relationship between two variables. Covariance is a measure of how two variables change in relation to each other.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Writing Equationsof Lines - Example 4

In mathematics, a line is a straight (geodesic) curve.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Absolute Value Functions - Example 2

In mathematics, the absolute value or modulus |x| of a real number "x" is the non-negative value of "x" without regard to its sign. That is, if "x" > 0, then |x| = x; if "x" = 0, then |x| = 0; and if "x" < 0, then |x| = ?x. The absolute value of a real number is also known as its magnitude. The absolute value of a complex number z = x + iy is x^2 + y^2, where x^2 + y^2 = |x + iy| = x^2 + y^2 = |z|.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Linear Inequalitiesintwovariables - Example 4

In mathematics, a linear inequality is an inequality involving one or more linear functions.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Piecewise Functions - Example 4

In mathematics, a piecewise function is a function defined in such a way that its value depends on the value of another function, called the "piece", at a number of points. The definition of the function is divided into multiple cases, each of which gives rise to a different value. Piecewise functions are used in computer programming, and in many other fields.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Correlationand Best- Fitting Lines

In statistics, correlation and covariance are two measures of the statistical relationship between two random variables. Correlation is a measure of the strength and direction of the linear relationship between two variables. Covariance is a measure of how two variables change in relation to each other.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Linear Inequalitesintwovariables

A linear inequality in two variables is an inequality that relates two real numbers x and y, which are both greater than or equal to zero, and states that one of the real numbers is either greater than or less than the other.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Paralleland Perpendicular Lines

In geometry, two lines in a plane which do not intersect, and which are not parallel to each other, are said to be skew lines. In the 18th century it was noted by Leonhard Euler that skew lines on a sphere form an analogous family.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Piecewise Functions

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Absolute Value Functions - Example 1

In mathematics, the absolute value or modulus |x| of a real number "x" is the non-negative value of "x" without regard to its sign. That is, if "x" > 0, then |x| = x; if "x" = 0, then |x| = 0; and if "x" < 0, then |x| = ?x. The absolute value of a real number is also known as its magnitude. The absolute value of a complex number z = x + iy is x^2 + y^2, where x^2 + y^2 = |x + iy| = x^2 + y^2 = |z|.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Correlationand Best- Fitting Lines - Example 1

In statistics, correlation and covariance are two measures of the statistical relationship between two random variables. Correlation is a measure of the strength and direction of the linear relationship between two variables. Covariance is a measure of how two variables change in relation to each other.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Linear Inequalitiesintwovariables - Example 1

In mathematics, a linear inequality is an inequality involving one or more linear functions.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Paralleland Perpendicular Lines - Example 1

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Piecewise Functions - Example 1

In mathematics, a piecewise function is a function defined in such a way that its value depends on the value of another function, called the "piece", at a number of points. The definition of the function is divided into multiple cases, each of which gives rise to a different value. Piecewise functions are used in computer programming, and in many other fields.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Writing Equationsof Lines - Example 1

In mathematics, a line is a straight (geodesic) curv.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Linear Inequalitiesintwovariables - Example 2

In mathematics, a linear inequality is an inequality involving one or more linear functions.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Paralleland Perpendicular Lines - Example 2

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Piecewise Functions - Example 2

In mathematics, a piecewise function is a function defined in such a way that its value depends on the value of another function, called the "piece", at a number of points. The definition of the function is divided into multiple cases, each of which gives rise to a different value. Piecewise functions are used in computer programming, and in many other fields.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Writing Equationsof Lines - Example 2

In mathematics, a line is a straight (geodesic) curve.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Correlationand Best- Fitting Lines - Example 3

In statistics, correlation and covariance are two measures of the statistical relationship between two random variables. Correlation is a measure of the strength and direction of the linear relationship between two variables. Covariance is a measure of how two variables change in relation to each other.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Linear Inequalitiesintwovariables - Example 3

In mathematics, a linear inequality is an inequality involving one or more linear functions.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Paralleland Perpendicular Lines - Example 3

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Paralleland Perpendicular Lines - Example 3

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Writing Equationsof Lines - Example 3

In mathematics, a line is a straight (geodesic) curve.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Absolute Value Inequalities - Example 4

In mathematics, an absolute value inequality is an inequality involving the absolute value of a number. Absolute value inequalities are of the form "|x| > c", where "c" is a real number. In contrast to strict inequalities, the inequality "|x| > c" is not necessarily satisfied for all values of "x".

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Paralleland Perpendicular Lines - Example 4

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.

Whitney Dillinger

Mastering Linear Equations and Inequalities: Essential Techniques

Correlationand Best- Fitting Lines - Example 2

In statistics, correlation and covariance are two measures of the statistical relationship between two random variables. Correlation is a measure of the strength and direction of the linear relationship between two variables. Covariance is a measure of how two variables change in relation to each other.

Whitney Dillinger