Linear Equations and Inequalities

This course focuses on the concept of Linear Equations and Inequalities. The course goes on to cover the introduction of Linear Equations in One Variable and Quadratic Equations such as Solving a Quadratic equation by factoring, by the square root method, by completing the square, and by using the quadratic formula. It talks about complex numbers, Add and subtract complex numbers, Multiply complex numbers, and Divide complex numbers. The course concludes with the concept of solving equations by factoring, rational equations, radicals and with rational exponents. Inequalities are also discussed in this course, including how to solve and graph linear inequalities, how to solve and graph a compound inequality, and how to solve polynomial and rational inequalities using test points. The course ends with the concept of Equations and Inequalities Involving Absolute Value.

11 topics

366 lectures

Educators

Course Curriculum

Equations and Inequalities

35 videos

Linear Equations and Functions

20 videos

Linear Equations and Inequalities

28 videos

Systems of Equations and Inequalities

25 videos

Matrices and Determinants

40 videos

Quadratic Equations

10 videos

Quadratic Functions

60 videos

50 videos

Introduction to Trigonometry

44 videos

Applications of Trigonometric Functions

15 videos

Graphing Trigonometry Functions

39 videos

Linear Equations and Inequalities Lectures

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

Writing Equationsof Lines - Example 4

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

Whitney Dillinger

Linear Equations and Inequalities

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

Linear Equations and Inequalities

Linear Inequalitiesintwovariables - Example 4

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

Whitney Dillinger

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

Linear Inequalitiesintwovariables - Example 1

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

Whitney Dillinger

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

Writing Equationsof Lines - Example 1

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

Whitney Dillinger

Linear Equations and Inequalities

Linear Inequalitiesintwovariables - Example 2

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

Whitney Dillinger

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

Writing Equationsof Lines - Example 2

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

Whitney Dillinger

Linear Equations and Inequalities

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

Linear Equations and Inequalities

Linear Inequalitiesintwovariables - Example 3

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

Whitney Dillinger

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

Writing Equationsof Lines - Example 3

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

Whitney Dillinger

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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

Linear Equations and Inequalities

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