Properties of Real Numbers: I. State the property of equality exhibited in each. 1. a. 7=7_________________________________ b. –1/7=-1/7_________________________________ 2. a. If a=b and b=3, then a=3_________________________________ b. If 3+y=3+x, then y=x_________________________________ 3. a. If n=2a+b, then n+7=2a+b+7_________________________________ b. If =-4, then (a+b) + c= (a+b)-4_________________________________ 4. a. If r + 3 = 8, then r +3 + (-3)= 8 + (-3 )_________________________________ b. If x – 2 = 7, then x – = 7 + 2_________________________________ 5. a. If x = 4, then 3x = (3) (4)_________________________________ b. If 1/4x=7, then 4 (1/4) x = 4 (7)_________________________________

II. Use the given property to complete each statement. 1.a. Cummulative:(ax) (8)=_______________________________ b. Identity:(-43m) + 0=_______________________________ 2.a. Closure:(3)(4)=_______________________________ b.Associative(-2+3) + 4=_______________________________ 3.a. Inverse:9 (1/9)=_______________________________ b. Distributive( 2a-3b) (-6a)=_______________________________ 4.a. Identity1 (q) + 1 (r)_______________________________ b.Cummulative(32)+(-4)=_______________________________ 5.a. Associative[(3m) (-7p)] (5p)=_______________________________ b.Closure(-3)+(8)=_______________________________

III. Given the following mathematical statements and proofs, supply the appropriate property or theorem involved in each of the following steps: 1.a. Prove: = - 16 Proof: 14 – 30 = 14 = (-30)________________________________ =14 + [(-14) + (-16)]________________________________ =[ 14 + ((-14) + (-16)________________________________ = 0 + (-16)________________________________ =- 16________________________________ b. Prove: - 2/ - 3 – 2/3 Proof: -2/ (1/3)________________________________ = - 2 ( -1/3)________________________________ = 2 (1/3)________________________________ =2/3________________________________ 2. a. Prove: If x + b = a, then x = a – b Proof: ( x + b ) + ( -b) + a + (-b)________________________________ x + b { b + ( -b ) } = a + b (-b)________________________________ x + 0 = a + (-b)________________________________ x = a –b________________________________

REVIEW EXERCISES: I.Use the roster method to write each set. 1. { x/x is a whole number but not a natural numbers } 2. { x/x is a factor of 12 } 3. { x/x is a division of 51 } II.Label each statement as true or false < { 1, 3, 5 } 2. 3< { 1, 2, 3 } 3. All irrational numbers are real numbers. 4. Some integers are not irrational numbers. 5. The intersection between rational and irrational sets of numbers is zero. 6. The quotient of any number by zero is zero. 7. The set of natural numbers is also the set of integers.

Basic concepts of polynomials: Given: a. 2 –4x-7x-6x b. x-x-x-3 -5-x 1.The constant term is _____. 2.The coefficient of x term is _____. 3.The term of degree 2 is ____. 4.Write the expression as the sum of terms ___. 5.Write the polynomial in descending powers of x __. 6.The sign of the x term is ___. 7.The sign of the consistent term is __.

Multiple choice. Write the letter corresponding to the correct answer. If there is none, write N. 1.Simplify: -3 – {10-[6-(8-9)]-5}= a. –17b. –15c. –11d. 9 2.x+y/x is a. monomialb. binomialc. expression of two termsd. expression of one term Tell whether each statement is true always, sometimes, or never. 1.A trinomial is polynomial _______. 2.A trinomial is binomial ______. 3.A monomial has no numerical coefficient ______. 4.A constant term is of a degree of 1 ______./ 5.A polynomial of degree 4 has 4 terms. 6.A constant is monomial _____. 7.A binomial is trinomial_____. 8.A Polynomial is a trinomial____.

Simplify the following by removing the grouping symbols: 1.–{ 4x- (3y-16x)}- (3x-2y) 2.-{ 16x – (12-3x)}- 6y) 3.- [4y- {13x-(14y-2x)}-21)} 4.-4(x-3y)-3(3x+5y)-6x-8y) 5.2x-{-3-[(2x-y-3)-3]-5x-y}-2y 6.-{5y-{8x-(5y+12x)}-6y] 7.-{16- [6x-(10y-12x]-3} 8.-3(x-2y)-(3x+4y-2x-2y)

Subtract the sum of the second and third expressions from the first. a.) 3x-2y+8z, 12x-y-10z, 3x-y+7z b.) 8x-y+5z, 2x+3y-6z, 5x-3y Subtract from the first from the sum of the second and expressions. a.) 2x-y-3, 4x=y-5, x+11y-8 b.) x-3y+9, 3x-7y+2, 3x+9,3x-7y+2, 3x+5y-6