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Workbook

Write the pH ranges as inequalities and label the substance as acidic or alkaline.

a) Lemon juice: 2,2 through 2,4; inclusive
b) Eggs: 7,6 through 8,0; inclusive
c) Carbonated soft drinks: 3,0 through 3,5; inclusive
d) Milk: 6,6 through 6,9; inclusive

Properties of Inequality:

For any two real numbers a and b, exactly one of the following is true:
a b , a b , a b   (Trichotomy Property)

Leta,b,c,d .

1) If a b and b c then a c   (Transitive Ex:

property)

2) a b  a c b c   Ex:

a b  Ex:
3)   a c b d  
c d 

i) a b and c 0   a.c b.c Ex:
4)
ii) a b and c 0   a.c b.c

1 1
5) If a and b have the same sign; a b   Ex:
a b

6) If n 1 and 0 a 1 then a   n  a . Ex:

7) If n 1 and a 1 then a  n  a . Ex:

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