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May 23rd

May 23rd

# 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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