Linear Equations and Inequalities in One Variable

LINEAR EQUATIONS and INEQUALITIES in ONE VARIABLE

Linear equations and Inequalities in One Variable Equation and Inequalities are relations between two quantities.

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Solution Set of a Linear Equation ,[object Object],[object Object],[object Object],[object Object]

B. x – 4 < 3 this statement is either true or false If x =6, then x – 4 is true because 6 – 4 < 3 If x = 10 , then x – 4 is false because 6 – 4 is not < 3 ,[object Object]

Solution Set of Simple Equations and Inequalities in One Variable by Inspection ,[object Object]

A. Guess-and-Check ,[object Object]

Consider the inequality x – 12 < 4 If x = 18, then 18 – 12 is not < 4 If x = 17, then 17 – 12 is not < 4 If x = 16, then 16 – 12 is not < 4 If x = 15, then 15 – 12 < 4 If x = 14, then 14 – 12 < 4 ,[object Object]

Another example ,[object Object],[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object]

C. Working Backwards ,[object Object]

Consider the equation 2x + 6 = 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],x

Example: 4y = 12 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],y

Properties of Equality and Inequality

Properties of Equality ,[object Object],[object Object],[object Object],[object Object]

B. Symmetric Property ,[object Object],[object Object],[object Object],[object Object]

C. Transitive Property ,[object Object],[object Object],[object Object],[object Object],[object Object]

D. Addition Property ,[object Object],[object Object]

E. Subtraction Property ,[object Object],[object Object]

F. Multiplication Property ,[object Object],[object Object]

G. Division Property ,[object Object],[object Object]

Properties of Inequality ,[object Object],[object Object]

A. Addition Property ,[object Object],[object Object]

B. Subtraction Property ,[object Object],[object Object]

C. Multiplication Property ,[object Object],[object Object],[object Object],[object Object]

D. Division Property ,[object Object],[object Object],[object Object],[object Object]

Solving Linear Equations in One Variable

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Solving Linear Inequalities in One Variable

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Solving Word Problems Involving Linear Equations

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Linear Equations and Inequalities in One Variable

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Linear Equations and Inequalities in One Variable