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 Scales Keeping the Balance

2x - 4 = 8

2x - 4 + 4 = 8 + 4 (Addition Property of =)

2x = 12 (Simplification)

1 * 2x = 1 * 12 (Multiplication Property of =)

2

2

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.)

2

2

x < -6 (Simplification)

Check --- Try any number less than -6.

-2(-7) - 4 > 8

Polya’s Problem Solving Steps

Understanding the Problem Devising a Plan Carrying out the Plan Looking Back

Pages 19-36 in Text

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

New Stamps’ Table

# of Stamps (n) Cost (c)

5 .34 * 5

10 .34 * 10

n .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