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MAT 202 - Section 7.1. By Dr. Marinas. Properties of Equalities. If a= b and b =c, then a=c. (Transitive Prop.) If a=b, then a + c = b + c . (Addition Prop.) If a=b, then a c = b c . (Multiplication Prop.). Equality Scales Keeping the Balance. 2x - 4 = 8

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## MAT 202 - Section 7.1

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**MAT 202 - Section 7.1**By Dr. Marinas**Properties of Equalities**• If a=b and b=c, then a=c. (Transitive Prop.) • If a=b, then a + c = b + c. (Addition Prop.) • If a=b, then ac = bc. (Multiplication Prop.)**Equality ScalesKeeping the Balance**2x - 4 = 8 2x - 4 + 4 = 8 + 4 (Addition Property of =) 2x = 12 (Simplification) 1 * 2x = 1 * 12 (Multiplication Property of =) 22 x = 6 (Simplification) Check 2(6) - 4 = 8**Properties of Inequalities**• If a>b and b>c, then a>c. (Transitive Prop.) • If a>b, then a + c > b + c. (Addition Prop.) • If a>b and c>0, then ac > bc. (Multiplication Prop.) • If a>b and c<0, then ac < bc. (Multiplication Prop.)**Inequality**-2x - 4 > 8 -2x - 4 + 4 > 8 + 4 (Addition Prop. of Ineq.) -2x > 12 (Simplification) -1 * -2x < -1 * 12 (Mult. Prop. of Ineq.) 22 x < -6 (Simplification) Check --- Try any number less than -6. -2(-7) - 4 > 8**Understanding the Problem**Devising a Plan Carrying out the Plan Looking Back Pages 19-36 in Text Polya’s Problem Solving Steps**New First Class Stamps**• What is the new cost of a stamp? 34 cents each • How much would 5 stamps cost? .34 * 5 = $1.70 • How much would 10 stamps cost? .34 * 10 = $3.40 • How much would “n” stamps cost? .34 n**Formula for Stamps**• Find a formula for Cost (c) in terms of Number of Stamps (n). c = .34n • Find a formula for Number of Stamps (n) in terms of Cost (c). n = c/.34 • How did you get these formulas?**Textbook Problems Page 349**• #2 Weight on Earth and Pluto • #5 - #7 Temperature Scales • #8 Salaries • Read Section 7-2

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