 # Lesson 3: Properties of equality and solving equations.

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Lesson 3: Properties of equality and solving equations

By the end of class you should be able to: Apply the properties of equality to solve single-step and multi-step linear equations Check a solution to a linear equation

Properties of equality Addition Propertyif a = b, then a + c = b + c Subtraction Propertyif a = b, then a – c = b – c Multiplication Propertyif a = b, then ac = bc Division Propertyif a = b, then Substitution Property if a = b, then either a or b may be substituted for the other in any equation (or inequality)

Properties of equality (cont’d) Reflexive Propertya = a Symmetric Propertyif a = b, then b = a Transitive Property if a = b, and b = c, then a = c Distributive Propertya(b + c) = ab + ac

What does it mean to find the solution to an equation? Determine the value for x such that when substituted back into the original equation, the resulting sentence is true.

Solving equations Solve: x + 6= -2

Solving equations (cont’d)

How to check a solution Substitute the solution candidate into the original equation Simplify both sides of the equal sign separately (do not pass terms across the equal sign) Compare the end result of each side for equality.