Courses tagged with "Customer Service Certification Program" (283)

Understanding absolute value and solving absolute value equations and inequalities. Absolute Value and Number Lines. Absolute Value 1. Absolute Value of Integers. Comparing Absolute Values. CA Algebra I: Number Properties and Absolute Value. Absolute Value Equations. Absolute Value Equations Example 1. Absolute Value Equation Example 2. U02_L2_T2_we1 Absolute Value Equations.avi. Absolute Value Inequalities. Absolute value inequalities Example 1. Absolute Inequalities 2. Absolute value inequalities example 3.

Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years.

Learn the fundamentals of digital signal processing theory and discover the myriad ways DSP makes everyday life more productive and fun.

Understanding and solving logarithms, including natural logs. Introduction to Logarithms. Logarithm of a Power. Sum of Logarithms with Same Base. Introduction to logarithm properties. Introduction to logarithm properties (part 2). Using Multiple Logarithm Properties to Simplify. Change of Base Formula. Logarithmic Scale. Richter Scale. Logarithmic Equations. Solving Logarithmic Equations. Proof: log a + log b = log ab. Proof: log_a (B) = (log_x (B))/(log_x (A)). Proof: A(log B) = log (B^A), log A - log B = log (A/B). Natural Logarithm with a Calculator. Calculator for Natural Logarithms. Graphing Natural Logarithm Function.

Learn about General Game Playing (GGP) and develop GGP programs capable of competing against humans and other programs in GGP competitions .

This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures. Part I covers generating functions and real asymptotics and then introduces the symbolic method in the context of applications in the analysis of algorithms and basic structures such as permutations, trees, strings, words, and mappings.

This class presents the fundamental probability and statistical concepts used in elementary data analysis. It will be taught at an introductory level for students with junior or senior college-level mathematical training including a working knowledge of calculus. A small amount of linear algebra and programming are useful for the class, but not required.

Introduction to statistics. We start with the basics of reading and interpretting data and then build into descriptive and inferential statistics that are typically covered in an introductory course on the subject. Overview of Khan Academy statistics. Statistics intro: mean, median and mode. Constructing a box-and-whisker plot. Sample mean versus population mean.. Variance of a population. Sample variance. Review and intuition why we divide by n-1 for the unbiased sample variance. Simulation showing bias in sample variance. Simulation providing evidence that (n-1) gives us unbiased estimate. Statistics: Standard Deviation. Statistics: Alternate Variance Formulas. Introduction to Random Variables. Probability Density Functions. Binomial Distribution 1. Binomial Distribution 2. Binomial Distribution 3. Binomial Distribution 4. Expected Value: E(X). Expected Value of Binomial Distribution. Poisson Process 1. Poisson Process 2. Introduction to the Normal Distribution. Normal Distribution Excel Exercise. Law of Large Numbers. ck12.org Normal Distribution Problems: Qualitative sense of normal distributions. ck12.org Normal Distribution Problems: Empirical Rule. ck12.org Normal Distribution Problems: z-score. ck12.org Exercise: Standard Normal Distribution and the Empirical Rule. ck12.org: More Empirical Rule and Z-score practice. Central Limit Theorem. Sampling Distribution of the Sample Mean. Sampling Distribution of the Sample Mean 2. Standard Error of the Mean. Sampling Distribution Example Problem. Confidence Interval 1. Confidence Interval Example. Mean and Variance of Bernoulli Distribution Example. Bernoulli Distribution Mean and Variance Formulas. Margin of Error 1. Margin of Error 2. Small Sample Size Confidence Intervals. Hypothesis Testing and P-values. One-Tailed and Two-Tailed Tests. Z-statistics vs. T-statistics. Type 1 Errors. Small Sample Hypothesis Test. T-Statistic Confidence Interval. Large Sample Proportion Hypothesis Testing. Variance of Differences of Random Variables. Difference of Sample Means Distribution. Confidence Interval of Difference of Means. Clarification of Confidence Interval of Difference of Means. Hypothesis Test for Difference of Means. Comparing Population Proportions 1. Comparing Population Proportions 2. Hypothesis Test Comparing Population Proportions. Squared Error of Regression Line. Proof (Part 1) Minimizing Squared Error to Regression Line. Proof Part 2 Minimizing Squared Error to Line. Proof (Part 3) Minimizing Squared Error to Regression Line. Proof (Part 4) Minimizing Squared Error to Regression Line. Regression Line Example. Second Regression Example. R-Squared or Coefficient of Determination. Calculating R-Squared. Covariance and the Regression Line. Correlation and Causality. Chi-Square Distribution Introduction. Pearson's Chi Square Test (Goodness of Fit). Contingency Table Chi-Square Test. ANOVA 1 - Calculating SST (Total Sum of Squares). ANOVA 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).avi. ANOVA 3 -Hypothesis Test with F-Statistic. Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance. Mean Median and Mode. Range and Mid-range. Reading Pictographs. Reading Bar Graphs. Reading Line Graphs. Reading Pie Graphs (Circle Graphs). Misleading Line Graphs. Stem-and-leaf Plots. Box-and-Whisker Plots. Reading Box-and-Whisker Plots. Statistics: The Average. Statistics: Variance of a Population. Statistics: Sample Variance. Deductive Reasoning 1. Deductive Reasoning 2. Deductive Reasoning 3. Inductive Reasoning 1. Inductive Reasoning 2. Inductive Reasoning 3. Inductive Patterns.

Solving and writing algebraic ratios and proportions. Solving rational equations. Introduction to Ratios (new HD version). Understanding Proportions. Ratios as Fractions in Simplest Form. Simplifying Rates and Ratios. Find an Unknown in a Proportion. Ratio and Proportion. Find an Unknown in a Proportion 2. Another Take on the Rate Problem. Finding Unit Rates. Finding Unit Prices. Writing Proportions. Ratio problem with basic algebra (new HD). More advanced ratio problem--with Algebra (HD version). Alternate Solution to Ratio Problem (HD Version). Advanced ratio problems. Unit conversion. Conversion between metric units. Converting within the metric system. Converting pounds to ounces. Converting Gallons to quarts pints and cups. Converting Farenheit to Celsius. Comparing Celsius and Farenheit temperature scales. Applying the Metric System. U.S. Customary and Metric units. Converting Yards into Inches. Unit Conversion with Fractions. Performing arithmetic calculations on units of volume. Application problems involving units of weight. Solving application problems involving units of volume. Unit Conversion Example: Drug Dosage. Perimeter and Unit Conversion. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Extraneous Solutions to Rational Equations. Rational Inequalities 2.

Identifying, solving, and graphing various types of functions. What is a function. Difference between Equations and Functions. Function example problems. Ex: Constructing a function. Understanding Function Notation Example 1). Understanding Function Notation Example 2). Understanding Function Notation Example 3). Understanding function notation. Testing if a relationship is a function. Graphical Relations and Functions. Functions as Graphs. Recognizing functions (example 1). Recognizing functions (example 2). Recognizing functions. Relations and Functions. Functional Relationships 1. Recognizing functions (example 3). Recognizing functions (example 4). Recognizing functions (example 5). Recognizing functions 2. Domain of a function. Domain and Range of a Relation. Domain and Range of a Function Given a Formula. Domain and Range 1. Domain of a Radical Function. Domain of a function. Domain and Range 2. Domain and Range of a Function. Range of a function. Domain and range from graphs. Domain and range from graph. Direct and Inverse Variation. Recognizing Direct and Inverse Variation. Proportionality Constant for Direct Variation. Direct and inverse variation. Direct Variation Models. Direct Variation 1. Inverse Variation Application. Direct Inverse and Joint Variation. Direct Variation Application. Ex 1: Evaluating a function. Ex 2: Graphing a basic function. Graphing a parabola with a table of values. Ex 4: Graphing radical functions. Ex: Graphing exponential functions. Views of a function. Interpreting a graph exercise example. Interpreting graphs of linear and nonlinear functions. Quotient of Functions. Sum of Functions. Product of Functions. Difference of Functions. Evaluating a function expression. Evaluating expressions with function notation. Evaluating composite functions example. Evaluating composite functions. Introduction to Function Inverses. Function Inverse Example 1. Function Inverses Example 2. Function Inverses Example 3. Inverses of functions. New operator definitions. New operator definitions 1. New operator definitions 2. New operator definitions 2. Introduction to functions. Functions Part 2. Functions (Part III). Functions (part 4). What is a function. Difference between Equations and Functions. Function example problems. Ex: Constructing a function. Understanding Function Notation Example 1). Understanding Function Notation Example 2). Understanding Function Notation Example 3). Understanding function notation. Testing if a relationship is a function. Graphical Relations and Functions. Functions as Graphs. Recognizing functions (example 1). Recognizing functions (example 2). Recognizing functions. Relations and Functions. Functional Relationships 1. Recognizing functions (example 3). Recognizing functions (example 4). Recognizing functions (example 5). Recognizing functions 2. Domain of a function. Domain and Range of a Relation. Domain and Range of a Function Given a Formula. Domain and Range 1. Domain of a Radical Function. Domain of a function. Domain and Range 2. Domain and Range of a Function. Range of a function. Domain and range from graphs. Domain and range from graph. Direct and Inverse Variation. Recognizing Direct and Inverse Variation. Proportionality Constant for Direct Variation. Direct and inverse variation. Direct Variation Models. Direct Variation 1. Inverse Variation Application. Direct Inverse and Joint Variation. Direct Variation Application. Ex 1: Evaluating a function. Ex 2: Graphing a basic function. Graphing a parabola with a table of values. Ex 4: Graphing radical functions. Ex: Graphing exponential functions. Views of a function. Interpreting a graph exercise example. Interpreting graphs of linear and nonlinear functions. Quotient of Functions. Sum of Functions. Product of Functions. Difference of Functions. Evaluating a function expression. Evaluating expressions with function notation. Evaluating composite functions example. Evaluating composite functions. Introduction to Function Inverses. Function Inverse Example 1. Function Inverses Example 2. Function Inverses Example 3. Inverses of functions. New operator definitions. New operator definitions 1. New operator definitions 2. New operator definitions 2. Introduction to functions. Functions Part 2. Functions (Part III). Functions (part 4).

Identifying and graphing circles, ellipses, parabolas, and hyperbolas. Introduction to Conic Sections. Recognizing conic sections. Conic Sections: Intro to Circles. Graphing circles. Equation of a circle in factored form. Completing the square to write equation in standard form of a circle. Equation of a circle in non-factored form. Graphing circles 2. Conic Sections: Intro to Ellipses. Equation of an ellipse. Foci of an Ellipse. Shifting and scaling parabolas. Parabola intuition example 1. Parabola intuition 1. Parabola Focus and Directrix 1. Focus and Directrix of a Parabola 2. Parabola intuition 2. Conic Sections: Intro to Hyperbolas. Conic Sections: Hyperbolas 2. Conic Sections: Hyperbolas 3. Equation of a hyperbola. Foci of a Hyperbola. Proof: Hyperbola Foci. Identifying an ellipse from equation. Identifying a hyperbola from an equation. Identifying circles and parabolas from equations. Hyperbola and parabola examples. Introduction to Conic Sections. Recognizing conic sections. Conic Sections: Intro to Circles. Graphing circles. Equation of a circle in factored form. Completing the square to write equation in standard form of a circle. Equation of a circle in non-factored form. Graphing circles 2. Conic Sections: Intro to Ellipses. Equation of an ellipse. Foci of an Ellipse. Shifting and scaling parabolas. Parabola intuition example 1. Parabola intuition 1. Parabola Focus and Directrix 1. Focus and Directrix of a Parabola 2. Parabola intuition 2. Conic Sections: Intro to Hyperbolas. Conic Sections: Hyperbolas 2. Conic Sections: Hyperbolas 3. Equation of a hyperbola. Foci of a Hyperbola. Proof: Hyperbola Foci. Identifying an ellipse from equation. Identifying a hyperbola from an equation. Identifying circles and parabolas from equations. Hyperbola and parabola examples.

Understanding how the brain works is one of the fundamental challenges in science today. This course will introduce you to basic computational techniques for analyzing, modeling, and understanding the behavior of cells and circuits in the brain. You do not need to have any prior background in neuroscience to take this course.

This course covers mathematical topics in algebra and trigonometry and is designed to prepare students to enroll for a first semester course in single variable calculus.

Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra. Introduction to matrices. Matrix multiplication (part 1). Matrix multiplication (part 2). Idea Behind Inverting a 2x2 Matrix. Inverting matrices (part 2). Inverting Matrices (part 3). Matrices to solve a system of equations. Matrices to solve a vector combination problem. Singular Matrices. 3-variable linear equations (part 1). Solving 3 Equations with 3 Unknowns. Introduction to Vectors. Vector Examples. Parametric Representations of Lines. Linear Combinations and Span. Introduction to Linear Independence. More on linear independence. Span and Linear Independence Example. Linear Subspaces. Basis of a Subspace. Vector Dot Product and Vector Length. Proving Vector Dot Product Properties. Proof of the Cauchy-Schwarz Inequality. Vector Triangle Inequality. Defining the angle between vectors. Defining a plane in R3 with a point and normal vector. Cross Product Introduction. Proof: Relationship between cross product and sin of angle. Dot and Cross Product Comparison/Intuition. Matrices: Reduced Row Echelon Form 1. Matrices: Reduced Row Echelon Form 2. Matrices: Reduced Row Echelon Form 3. Matrix Vector Products. Introduction to the Null Space of a Matrix. Null Space 2: Calculating the null space of a matrix. Null Space 3: Relation to Linear Independence. Column Space of a Matrix. Null Space and Column Space Basis. Visualizing a Column Space as a Plane in R3. Proof: Any subspace basis has same number of elements. Dimension of the Null Space or Nullity. Dimension of the Column Space or Rank. Showing relation between basis cols and pivot cols. Showing that the candidate basis does span C(A). A more formal understanding of functions. Vector Transformations. Linear Transformations. Matrix Vector Products as Linear Transformations. Linear Transformations as Matrix Vector Products. Image of a subset under a transformation. im(T): Image of a Transformation. Preimage of a set. Preimage and Kernel Example. Sums and Scalar Multiples of Linear Transformations. More on Matrix Addition and Scalar Multiplication. Linear Transformation Examples: Scaling and Reflections. Linear Transformation Examples: Rotations in R2. Rotation in R3 around the X-axis. Unit Vectors. Introduction to Projections. Expressing a Projection on to a line as a Matrix Vector prod. Compositions of Linear Transformations 1. Compositions of Linear Transformations 2. Matrix Product Examples. Matrix Product Associativity. Distributive Property of Matrix Products. Introduction to the inverse of a function. Proof: Invertibility implies a unique solution to f(x)=y. Surjective (onto) and Injective (one-to-one) functions. Relating invertibility to being onto and one-to-one. Determining whether a transformation is onto. Exploring the solution set of Ax=b. Matrix condition for one-to-one trans. Simplifying conditions for invertibility. Showing that Inverses are Linear. Deriving a method for determining inverses. Example of Finding Matrix Inverse. Formula for 2x2 inverse. 3x3 Determinant. nxn Determinant. Determinants along other rows/cols. Rule of Sarrus of Determinants. Determinant when row multiplied by scalar. (correction) scalar multiplication of row. Determinant when row is added. Duplicate Row Determinant. Determinant after row operations. Upper Triangular Determinant. Simpler 4x4 determinant. Determinant and area of a parallelogram. Determinant as Scaling Factor. Transpose of a Matrix. Determinant of Transpose. Transpose of a Matrix Product. Transposes of sums and inverses. Transpose of a Vector. Rowspace and Left Nullspace. Visualizations of Left Nullspace and Rowspace. Orthogonal Complements. Rank(A) = Rank(transpose of A). dim(V) + dim(orthogonal complement of V)=n. Representing vectors in Rn using subspace members. Orthogonal Complement of the Orthogonal Complement. Orthogonal Complement of the Nullspace. Unique rowspace solution to Ax=b. Rowspace Solution to Ax=b example. Showing that A-transpose x A is invertible. Projections onto Subspaces. Visualizing a projection onto a plane. A Projection onto a Subspace is a Linear Transforma. Subspace Projection Matrix Example. Another Example of a Projection Matrix. Projection is closest vector in subspace. Least Squares Approximation. Least Squares Examples. Another Least Squares Example. Coordinates with Respect to a Basis. Change of Basis Matrix. Invertible Change of Basis Matrix. Transformation Matrix with Respect to a Basis. Alternate Basis Transformation Matrix Example. Alternate Basis Transformation Matrix Example Part 2. Changing coordinate systems to help find a transformation matrix. Introduction to Orthonormal Bases. Coordinates with respect to orthonormal bases. Projections onto subspaces with orthonormal bases. Finding projection onto subspace with orthonormal basis example. Example using orthogonal change-of-basis matrix to find transformation matrix. Orthogonal matrices preserve angles and lengths. The Gram-Schmidt Process. Gram-Schmidt Process Example. Gram-Schmidt example with 3 basis vectors. Introduction to Eigenvalues and Eigenvectors. Proof of formula for determining Eigenvalues. Example solving for the eigenvalues of a 2x2 matrix. Finding Eigenvectors and Eigenspaces example. Eigenvalues of a 3x3 matrix. Eigenvectors and Eigenspaces for a 3x3 matrix. Showing that an eigenbasis makes for good coordinate systems. Vector Triple Product Expansion (very optional). Normal vector from plane equation. Point distance to plane. Distance Between Planes.

Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus playlist before starting here. What is a differential equation. Separable Differential Equations. Separable differential equations 2. Exact Equations Intuition 1 (proofy). Exact Equations Intuition 2 (proofy). Exact Equations Example 1. Exact Equations Example 2. Exact Equations Example 3. Integrating factors 1. Integrating factors 2. First order homegenous equations. First order homogeneous equations 2. 2nd Order Linear Homogeneous Differential Equations 1. 2nd Order Linear Homogeneous Differential Equations 2. 2nd Order Linear Homogeneous Differential Equations 3. 2nd Order Linear Homogeneous Differential Equations 4. Complex roots of the characteristic equations 1. Complex roots of the characteristic equations 2. Complex roots of the characteristic equations 3. Repeated roots of the characteristic equation. Repeated roots of the characteristic equations part 2. Undetermined Coefficients 1. Undetermined Coefficients 2. Undetermined Coefficients 3. Undetermined Coefficients 4. Laplace Transform 1. Laplace Transform 2. Laplace Transform 3 (L{sin(at)}). Laplace Transform 4. Laplace Transform 5. Laplace Transform 6. Laplace Transform to solve an equation. Laplace Transform solves an equation 2. More Laplace Transform tools. Using the Laplace Transform to solve a nonhomogeneous eq. Laplace Transform of : L{t}. Laplace Transform of t^n: L{t^n}. Laplace Transform of the Unit Step Function. Inverse Laplace Examples. Laplace/Step Function Differential Equation. Dirac Delta Function. Laplace Transform of the Dirac Delta Function. Introduction to the Convolution. The Convolution and the Laplace Transform. Using the Convolution Theorem to Solve an Initial Value Prob.

An introduction to dynamical modeling techniques used in contemporary Systems Biology research.

Logarithms. Ex: Converting an exponential to logarithmic statement. Evaluating logarithms. Fancier logarithm expressions. Evaluating logarithms 2. Graphing Logarithmic Functions. Introduction to Logarithms. Introduction to logarithm properties. Introduction to logarithm properties (part 2). Logarithm of a Power. Sum of Logarithms with Same Base. Using Multiple Logarithm Properties to Simplify. Operations with logarithms. Change of Base Formula. Proof: log a + log b = log ab. Proof: A(log B) = log (B^A), log A - log B = log (A/B). Change of base formula proof. Logarithmic Equations. Solving Logarithmic Equations. Solving Logarithmic Equations. Logarithmic Scale. Richter Scale. Natural Logarithm with a Calculator. Calculator for Natural Logarithms. Graphing Natural Logarithm Function. Logarithms. Ex: Converting an exponential to logarithmic statement. Evaluating logarithms. Fancier logarithm expressions. Evaluating logarithms 2. Graphing Logarithmic Functions. Introduction to Logarithms. Introduction to logarithm properties. Introduction to logarithm properties (part 2). Logarithm of a Power. Sum of Logarithms with Same Base. Using Multiple Logarithm Properties to Simplify. Operations with logarithms. Change of Base Formula. Proof: log a + log b = log ab. Proof: A(log B) = log (B^A), log A - log B = log (A/B). Change of base formula proof. Logarithmic Equations. Solving Logarithmic Equations. Solving Logarithmic Equations. Logarithmic Scale. Richter Scale. Natural Logarithm with a Calculator. Calculator for Natural Logarithms. Graphing Natural Logarithm Function.

Calculus One is a first introduction to differential and integral calculus, emphasizing engaging examples from everyday life.

Solving exponential and radical expressions and equations. Using scientific notation and significant figures. Negative and Positive Exponents. Evaluating exponential expressions. Evaluating exponential expressions 3. Exponent Rules Part 1. Exponent Rules Part 2. Exponent Properties 1. Exponent Properties 2. Exponent Properties 3. Exponent Properties 4. Simplifying rational expression with exponent properties. Exponent Properties 5. Exponent Properties 6. Exponent Properties 7. Simplifying Square Roots. Simplifying Square Roots Comment Response. Radical Equivalent to Rational Exponents. Radical Equivalent to Rational Exponents 2. Radical Expressions with Higher Roots. Adding and Simplifying Radicals. Subtracting and Simplifying Radicals. Multiply and Simplify a Radical Expression 1. Multiply and Simplify a Radical Expression 2. Exponent Properties Involving Products. Rational Exponents and Exponent Laws. Simplifying Cube Roots. More Rational Exponents and Exponent Laws. How to Rationalize a Denominator. Simplifying Expressions with Exponents. Simplifying Expressions with Exponents 2. Simplifying Expressions with Exponents 3. Fractional Exponent Expressions 1. Fractional Exponent Expressions 2. Fractional Exponent Expressions 3. Simplifying expressions with exponents. Solving Radical Equations. Extraneous Solutions to Radical Equations. Solving Radical Equations 1. Solving Radical Equations 2. Solving Radical Equations 3. Applying Radical Equations 1. Applying Radical Equations 2. Applying Radical Equations 3. Radical equations. Negative and Positive Exponents. Evaluating exponential expressions. Evaluating exponential expressions 3. Exponent Rules Part 1. Exponent Rules Part 2. Exponent Properties 1. Exponent Properties 2. Exponent Properties 3. Exponent Properties 4. Simplifying rational expression with exponent properties. Exponent Properties 5. Exponent Properties 6. Exponent Properties 7. Simplifying Square Roots. Simplifying Square Roots Comment Response. Radical Equivalent to Rational Exponents. Radical Equivalent to Rational Exponents 2. Radical Expressions with Higher Roots. Adding and Simplifying Radicals. Subtracting and Simplifying Radicals. Multiply and Simplify a Radical Expression 1. Multiply and Simplify a Radical Expression 2. Exponent Properties Involving Products. Rational Exponents and Exponent Laws. Simplifying Cube Roots. More Rational Exponents and Exponent Laws. How to Rationalize a Denominator. Simplifying Expressions with Exponents. Simplifying Expressions with Exponents 2. Simplifying Expressions with Exponents 3. Fractional Exponent Expressions 1. Fractional Exponent Expressions 2. Fractional Exponent Expressions 3. Simplifying expressions with exponents. Solving Radical Equations. Extraneous Solutions to Radical Equations. Solving Radical Equations 1. Solving Radical Equations 2. Solving Radical Equations 3. Applying Radical Equations 1. Applying Radical Equations 2. Applying Radical Equations 3. Radical equations.

Exploring a world where both sides aren't equal anymore!. Inequalities Using Multiplication and Division. One-step inequality with multiplication and division example. Constructing and solving one-step inequality. One step inequalities. One-Step inequality involving addition. Inequalities Using Addition and Subtraction. Two-step inequality example. Multi-Step Inequalities. Multi-Step Inequalities 2. Multi-Step Inequalities 3. Multi-step linear inequalities. Interpreting Inequalities. Writing and using inequalities 2. Writing and using inequalities 3. Interpreting and solving linear inequalities. Inequality examples. Compound Inequalities. Compound Inequalities. Compound Inequalities 2. Compound Inequalities 3. Compound Inequalities 4. Compound inequalities. Absolute Value Inequalities. Absolute value inequalities Example 1. Absolute Value Inequalities Example 2. Absolute value inequalities example 3. Writing and using inequalities. Dogs cats and bears in a pet store visual argument. Dogs cats and bears in a pet store analytic argument. Reasoning through inequality expressions. Using expressions to understand relationships. Structure in expressions 1. Inequalities Using Multiplication and Division. One-step inequality with multiplication and division example. Constructing and solving one-step inequality. One step inequalities. One-Step inequality involving addition. Inequalities Using Addition and Subtraction. Two-step inequality example. Multi-Step Inequalities. Multi-Step Inequalities 2. Multi-Step Inequalities 3. Multi-step linear inequalities. Interpreting Inequalities. Writing and using inequalities 2. Writing and using inequalities 3. Interpreting and solving linear inequalities. Inequality examples. Compound Inequalities. Compound Inequalities. Compound Inequalities 2. Compound Inequalities 3. Compound Inequalities 4. Compound inequalities. Absolute Value Inequalities. Absolute value inequalities Example 1. Absolute Value Inequalities Example 2. Absolute value inequalities example 3. Writing and using inequalities. Dogs cats and bears in a pet store visual argument. Dogs cats and bears in a pet store analytic argument. Reasoning through inequality expressions. Using expressions to understand relationships. Structure in expressions 1.