MATH10-1 COLLEGE ALGEBRA LINEAR EQUATIONS IN ONE VARIABLE AND APPLICATIONS
GENERAL OBJECTIVE • Classify equations as linear, fractional, or rational, • Solve linear equations, • Solve equations leading to the form ax + b = 0, and • Solve application problems involving linear equations by developing mathematical models for real-life problems. At the end of the lesson the students are expected to:
TODAY’S OBJECTIVE • Identify an equation, • Classify equations as identity, conditional or equivalent, • Distinguish a consistent from an inconsistent equation, • Enumerate the properties of equality. At the end of the lesson the students are expected to:
KINDS OF EQUATIONS 2
• Two equations with exactly the same solutions are called equivalent equations. Example: The following are equivalent equations. 4 . c 22 2 5 . b 20 5 . a x x x
EXAMPLEDetermine whether the given equation is an identity or aconditional equation. 15
For all real numbers a , b , and c 1 . Addition Property of Equality If a = b then a + c = b + c 2 . Subtraction Property of Equality If a = b then a – c = b – c 3 . Multiplication Property of Equality If a = b then a c = b c ∙ ∙ 4 . Division Property of Equality If a = b then PROPERTIES OF EQUALITY 0 where c c b c a
TODAY’S OBJECTIVE • Define linear equations in one variable, • Determine the difference between linear and nonlinear equations, • Enumerate the steps in solving linear equations, • Solve linear equations and equations involving fractions, • Solve rational equations which are reducible to linear equations, • Define extraneous solution. At the end of the lesson the students are expected to:
RECALL • An identity equation is an equation that is true for any number substituted to the variable. • An equation is a statement that two mathematical expressions are equivalent or equal. • A conditional equation is an equation that is true only for certain values of the unknown. • Two equations with exactly the same solutions are called equivalent equations. • An inconsistent equation is an equation that has no solution. • A consistent equation is an equation that has a solution.
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