Further Solving Linear Equations

Overview

• Section 2.3 in the textbook
– Solving Equations Containing Fractions
– Solving Equations Containing Decimals
– Identities & Contradictions

Solving Equations Containing
Fractions

Solving Equations with Fractions

• While it is certainly possible to work with
fractions in an equation , it is often easier to
eliminate them
• How do we add two UNLIKE fractions?
– Look for an LCD
• We can use the LCD to help us eliminate the
fractions in an equation
• What kind of mathematical statement is adding
½ + ¼?
– Ex pression

• The rules are a bit different with an
equation
• What must always be remembered when
performing ope rations on equations ?
– “What you do to one side , you must do to
the other”
• How can we use the LCD to help us solve
an equation with fractions?

Solving Equations with
Fractions (Example)

Ex 1: Solve:

Solving Equations with
Fractions (Example)

Ex 2: Solve:

Solving Equations with
Decimals

Solving Equations with Decimals

• Again, it is possible to work with decimals in
equations , but easier to eliminate them
• Consider 0.06, 3.3, and -2.19
• What is the least number of decimal places the
decimal must be moved so that ALL three
numbers become Integers?
• Moving the decimal point to the right by two
places is the same as doing what?
• What is the mantra when doing operations on an
equation ?

Solving Equations with
Decimals (Example)
Ex 3: Solve:

Identities & Contradictions

Identities & Contradictions

• Can only happen when the variable drops
out on BOTH sides of the equation
• De termine whether the resulting statement
is true or not:
– If yes, then the equation has an infinite
number of solutions and we say the solution is
the set of all real numbers
• Also called an identity
– If no, then the equation has no solution
• Also called a contradiction

Identities & Contradictions
(Example)

Ex 4: Solve:

Summary

• After studying these slides, you should
know how to do the fol lowing :
– Solving Equations with Fractions
– Solving Equations with Decimals
– Identities & Contradictions
• Additional Practice
– See the list of suggested problems for 2.3
• Next lesson
– Introduction to Problem Solving (Section 2.4)

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