MATH10-1 Lecture 9rev. - LINEAR EQUATIONS IN ONE VARIABLE AND APPLICATIONS MATH10-1 COLLEGE ALGEBRA GENERAL OBJECTIVE At the end of the lesson the

MATH10-1 Lecture 9rev. - LINEAR EQUATIONS IN ONE VARIABLE...

This preview shows page 1 - 14 out of 62 pages.

MATH10-1 COLLEGE ALGEBRA LINEAR EQUATIONS IN ONE VARIABLE AND APPLICATIONS
Image of page 1
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:
Image of page 2
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:
Image of page 3
DEFINITION EQUATION
Image of page 4
KINDS OF EQUATIONS 2
Image of page 5
Image of page 6
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
Image of page 7
Image of page 8
EXAMPLEDetermine whether the given equation is an identity or aconditional equation. 15
Image of page 9
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
Image of page 10
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:
Image of page 11
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.
Image of page 12
DEFINITION
Image of page 13
Image of page 14

You've reached the end of your free preview.

Want to read all 62 pages?

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture