Name________________________________________________ Date_________________________ Algebra I – Pd ____ Real Numbers and Properties 1A

Real Numbers

Real numbers are divided into two types, rational numbers and irrational numbers

I. Rational Numbers: Any number that can be expressed as the quotient of two integers. (fraction). Any number with a decimal that repeats or terminates. Subsets of Rational Numbers:

A. Integers : rational numbers that contain no fractions or decimals.{…,-2, -1, 0, 1, 2, …}

B. Whole Numbers : all positive integers and the number 0.{0, 1, 2, 3, … }

C. Natural Numbers (counting numbers) : all positive integers (not 0).{1, 2, 3, … }

II. Irrational Numbers: Any number that cannot be expressed as a quotient of two integers (fraction). Any number with a decimal that is non-repeating and non-terminal (doesn’t repeat and

doesn’t end). Most common example is π.

Properties

1) Commutative Properties of Addition and Multiplication: The order in which you add or multiply does not matter.

a + b = b + a and a b = b a∙ ∙2) Symmetric Property:

If a + b = c, then c = a + b If , then

3) Reflexive Property: a + b = a + b Nothing changes

4) Associative Properties of Addition and Multiplication. The grouping of addition and multiplication does not matter. (Parenthesis)

5) Transitive Property: If a = b and b = c, then a = c. If, and, then

6) Distributive Property: a (b + c) = ab + ac and a(b – c) = ab – ac

7) Additive Identity: When zero is added to any number or variable, the sum is the number or variable. a + 0 = a

8) Multiplicative Identity: When any number or variable is multiplied by 1, the product is the number or variable. a 1 = a∙

9) Multiplicative Property of Zero: When any number or variable is multiplied by zero, the product is 0. a 0 = 0∙

10) Additive Inverse: The opposite of a number. The sum of a number and its additive inverse is 0. The additive inverse of 5 is negative 5 because 5 + (-5) = 0 x + (-x) = 0

11) Multiplicative Inverse: The reciprocal of a number. The product of a number and its multiplicative inverse is 1.

The multiplicative inverse of 5 is 15 because 5( 1

5 )=1 x ( 1x )=1

Name___________________________________________ Date_________________________ Algebra I – Pd ____ Real Numbers and Properties 1B

Numbers Worksheet

Part 1 – Use an integer to express the number(s) in each application below:

1) Erin discovers that she has spent $53 more than she has in her checking account.________

2) The record high Fahrenheit temperature in the United States was 134˚ on July 10th, 1913. ________

3) A football team gained 5 yards _________, then lost 10 yards on the next play ________

4) The shore surrounding the Dead Sea is 1348 feet below sea level. ___________

Part 2 – Tell whether each statement is true or false. (write the entire word)

5) - 2 < 4 ____________ 6) 6 > - 3 ____________

7) - 9 < - 12 ____________ 8) - 4 ≥ - 1 ____________

9) - 6 ≤ 0 ____________ 10) - 15 > - 5 ____________

Part 3 – Write an example of a number that satisfies each given condition.

11) An integer between 3.6 and 4.6 ____________

12) A rational number between 2.8 and 2.9 ____________

13) A whole number that is not positive and is less than 1 ____________

14) A whole number that is greater than 3.5 ___________

15) A real number that is neither negative nor positive ____________

Part 4 – Circle the correct answer to the following questions.______16) Which number is a whole number but not a natural number? a) – 2 b) 3 c) ½ d) 0______17) Which number is an integer but not a whole number? a) – 5 b) ¼ c) 3 d) 2.5______18) Which number is irrational? a) π b) 4 c) .1875 d) .33Part 5 – Write an example down for the following questions.

19) Give an example of a number that is rational, but not an integer.

20) Give an example of a number that is an integer, but not a whole number.

21) Give an example of a number that is a whole number, but not a natural number. ___________

22) Give an example of a number that is a natural number, but not an integer.

Properties Worksheet

A. Complete the Matching Column (put the corresponding letter next to the number)1) If 18 = 13 + 5, then 13+5 = 18 a) Reflexive2) 6 · (2 · 5) = (6 · 2) · 5 b) Additive Identity 3) 3(9 + 2) = 3(9) + 3(2) c) Multiplicative identity4) 15 + (10 + 3) = (15 + 10) + 3 d) Associative Property of Mult.5) 50 · 1 = 50 e) Transitive6) 7 4 = 4 7∙ ∙ f) Associative Property of Add.7) 13 + 0 = 13 g) Symmetric8) 11 + 8 = 11 + 8 h) Commutative Property of Mult.9) If 30 + 34 = 64 and 64 = 82, then 30 + 34 = 82 I) Multiplicative property of zero10) 11 0 = 0∙ j) Distributive

______ 11) Which property is represented by: 5+ (4 + 7x) = (5 + 4) + 7x? a) Associative Property of Add. c) Distributive Propertyb) Commutative Property of Add. d) Symmetric Property

______ 12) Which property is illustrated by 5(a + 6) = 5(a) + 5(6)a) associative prop. of add. b) distributive c) transitive d) symmetric

______ 13) What is the formula for area of a rhombus?a) A = lh b) A = ½ h(b1 + b2) c) A = ½ d1d2 d) A = lwh

______ 14) What property is represented by: If 4 + 14 = 18 and 18 = 6 3, then 14 + 4 = 6 3 ?∙ ∙a) Symmetric Property c) Commutative Property of Add.b) Transitive Property d) Awesome Property

______ 15) Which property is represented by: 3 + 9 = 9 + 3?a) Transitive Property c) Reflexive Propertyb) Symmetric Property d) Commutative Property of Add.

______ 16) Which property is represented by: If 3 + 11 = 14, then 14 = 3 + 11?a) Transitive Property c) Reflexive Propertyb) Commutative Property of Add. d) Symmetric Property

17) Write a statement that illustrates the Additive Identity Property: ______________________________

18) Write a statement that illustrates the Multiplicative Identity Property: ________________________

19) Write a statement that illustrates the Symmetric Property: ______________________________

20) Write a statement that illustrates the Associative Property of Add.: ______________________________

Name____ANSWERS_______________________ Date_________________________ Algebra I – Pd ____ Real Numbers and Properties 1B

Numbers Worksheet

Part 1 – Use an integer to express the number(s) in each application below:

1) – 53 2) 134 3) 5 ,−10 4) −¿1348

Part 2 – Tell whether each statement is true or false. (write the entire word)

5) True 6) True 7) False 8) False 9) True 10) False

Part 3 – Write an example of a number that satisfies each given condition.

11) 4 12) 2.81 13) 0 14) 4 15) 0

Part 4 – Circle the correct answer to the following questions.

16) D 17) A 18) A

Part 5 – Write an example down for the following questions.

19) Decimal or Fraction 20) negatives 21)zero 22) not possible

Properties Worksheet

Matching Column: 1) G 2) D 3) J 4) F 5) C 6) H 7) B 8) A 9) E 10) I

Multiple Choice:11) A 12) B 13) C 14) B 15) D 16) D

17) Write a statement that illustrates the Additive Identity Property: ______________________________

18) Write a statement that illustrates the Multiplicative Identity Property: ________________________

19) Write a statement that illustrates the Symmetric Property: ______________________________

20) Write a statement that illustrates the Associative Property of Add.: ______________________________

Name___________________________________________ Date_________________________ Algebra I – Pd ____ Real Numbers and Properties 1C

Directions: You may answer of all the following questions on this paper.

1) State which property is being shown

a) 3(x + 5) = 3x + 3(5) __________________________________________b) (9 + 4) + 5 = 9 + (4 + 5) __________________________________________c) 36 0 = 0 ∙ __________________________________________d) 8m + 6m = m(8 + 6) __________________________________________e) (m 14) n = m (14 n)∙ ∙ ∙ ∙ __________________________________________f) 162 1 = 162∙ __________________________________________

g) 4 ∙( 14 ) = 1 __________________________________________

h) 5 + 8 = 8 + 5 __________________________________________

2) Complete the matching column

_____1) 5(6 + 2) = 5(6) + 5(2) a) Additive Identity _____ 2) If 40 = 4(10), then 4(10) = 40 b) Associative Property of Mult._____ 3)5 + 18 = 18 + 5 c) Commutative Property of Add._____ 4) 14 · 1 = 14 d) Distributive Property_____ 5) 15 + 2 = 15 + 2 e) Transitive Property_____ 6)(5 + 6) + 8 = 5 + (6 + 8) f) Multiplicative Identity_____ 7) If 62 = 36 and 36 = 4(9), then 62 = 4(9) g) Associative Property of Add._____ 8) 23 · 0 = 0 h) Multiplicative property of Zero

I) Commutative Property of Mult. j) Symmetric Property

k) Reflexive Property

3) Is the following operation true? If true, which property is being show, if false, explain why.

(8 ÷ 4) ÷ 2 = 8 ÷ (4 ÷ 2)

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_____ 4) Which is an illustration of the commutative property of addition?a) a + 0 = a b) a(b + c) = ab + acc) a + b = b + a d) (a + b) + c = a + (b + c)

_____ 5) Which statement illustrates the associative property of multiplication?

a) 2( 12 )=1 b) 2(3 + 4) = 2(3) + 2(4)

c) 2(3 · 4) = (2 · 3)4 d) 2(1) = 2

6) Give an example of each:

a) a number that is whole, but not a natural number ___________________________

b) a number that is rational, but not a whole number ___________________________

c) a number that is rational, but not an integer ___________________________

d) a number that is irrational ___________________________

e) a number that is a natural number, but not an integer ___________________________

f) a number that is an integer, but not a natural number ___________________________

7) Write True or False (do not write T or F… you must write out the whole word!)

a) all whole number are rational _____________________

b) all integers are natural numbers _____________________

c) all real numbers are rational _____________________

d) all irrational number are real _____________________

e) all natural numbers are irrational _____________________

Name____ANSWERS___________________________ Date_________________________ Algebra I – Pd ____ Real Numbers and Properties 1C

1) State which property is being showna) Distributive property b) Assoc. Prop. Of Add. c) Multi. Prop of Zerod) Distributive Property e) Assoc. Prop. Of Mult. f) Multi. Identityg) Multiplicative Inverse h) Comm. Prop of Add.

2) Complete the matching column1) D 2) J 3) C 4) F 5) K6) G 7) E 8) H

3) (8 ÷ 4) ÷ 2 = 8 ÷ (4 ÷ 2) False

4) C

5) C

6) Give an example of each:

a) a number that is whole, but not a natural number Zero

b) a number that is rational, but not a whole number Negatives or Decimals

c) a number that is rational, but not an integer Decimals or Fractions

d) a number that is irrational π √2√3

e) a number that is a natural number, but not an integer Not possible

f) a number that is an integer, but not a natural number Negatives or Zero

7) a) True b) False c) False d) True e) False

Name___________________________________________ Date_________________________ Algebra I – Pd ____ Evaluating Expressions 1D

When given an algebraic expression with one or more unknown variables, we cannot find the exact value of the expression. If we are told what the value(s) or the variable(s) are then we can find the exact value.

For Example: 13x + 2y Since we do not know the values of x and y we cannot simplify

If we are told to evaluate 13x + 2y when x = 3 and y = 4, we can substitute these values in.

First step: Write the expression 13x + 2ySecond step: Replace the variables 13(3) + 2(4) ** Always use parenthesisThird step: Simplify using PEMDAS 39 + 8 = 47

Errors often occur due to sloppiness and laziness, so be careful and be neat!!

Directions: Evaluate the following

1) 50 – 3x, when x = 7 1) _______________

2) 2 x2−5x+4 when x = 7 2) _______________

3) 2a5

+( n−1 ) d when a = 40, n = 10 and d = 3 3) _______________

4) (2 x )2−2x2 when x = 4 4) _______________

5) x2−8 y when x = 5 and y = 12 5) _______________

6) r2+4 s when r = 3 and s = 0.5 6) _______________

7) a2+b2−d2 when a = 8, b = 6, and d = 3 7) _______________

8) (3 w−2 x )2 when w = 10 and x = 8 8) _______________

9) 3 w2−2 x2 when w = 10 and x = 8 9) _______________

10) 59

( F−32 ) when F = 86 10) _______________

11) 12

x ( y+z) when x = 8, y = 5, and z = 2 11) _______________

Extra Examples:

Part 1 – Using your order of operations evaluate the expression.1) 5 + 2 – 3 2) 12 – 6 + 1 3) 10 · 2 ÷ 4

4) 4 + 3 · 2 5) 8 · 3 – 10 6) 5 – 14 ÷ 7

7) 2 + 36 ÷ 4 8) 10 ÷ 5 + 3 · 2 9) 4 – 20 ÷ 10 + 7

10) 3 · 22 + 1 11) 2 · 32 ÷ 3 12) 4(2 + 3) – 8

Part 2 – Using the given information, evaluate the expression.

13) 3 + 2x2, when x = 2 14) 30 – 3x2, when x = 3

15) 3a – 2b, when a = 2 and b = 3 16) 5x2 – y, when x = 3 and y = 5

17) 2x + x2 – 4, when x = 4 18) a3 – 3a + 5, when a = 2

19) a2 ÷ 5 + 3, when a = 5 20) x · y – 8, when x = 3 and y = 4

21) a2 – b ÷ 4, when a = 5 and b = 8 22) 3y – x2 · 4, when x = 2 and y = 6

23) 2 a+b

3 when a = 4 and b = 1 24) 7 – xy · 2, when x = 15 and y = 5

25)(2y + 6) – 4y, when y = 3 26) 5c – (2 + c), when c = 2

27) 2b(7 + b), when b = 1 28) (3x + 1)x, when x = 3

29) 3x(2y – 3), when x = 5 and y = 2 30) 3x + 2(2x + 5), when x = 1

31) 15 ÷ (2a + 1), when a = 1 32) (7x + 4) ÷ 2, when x = 2

33) x ÷ (2y + 1), when x = 21 and y = 1 34) b ÷ (3a – 2), when a = 2 and b = 16

35) (6a + 2) ÷ b, when a = 3 and b = 2 36) [10 – (2x ÷ 3)] + y, when x = 3 and y = 4

37) 8a2−10 b÷ (3 c )+4

2b2÷ (3 a−9) when a = −¿3, b = 6, and c = 2

38) [2 y2+8 x2÷ (−10 ) ]÷ 3 z4 x+6 y+8 y+2

when x = 5, y = 7, and z = −¿4

39) (a2+b2) ÷ (5c )10 b−7a−1

when a = −¿8, b = −¿6 and c = 4

Name________ANSWERS_______________________ Date_________________________ Algebra I – Pd ____ Evaluating Expressions 1D

Directions: Evaluate the following

1) 29 2) 67 3) 43 4)31 5) 21 6) 9.2

7) 91 8) 196 9) 172 10) 30 11) 28

Extra Examples:

Part 1 – Using your order of operations evaluate the expression.

1) 4 2) 7 3) 5 4) 10 5) 14 6) 3

7) 11 8) 8 9) 9 10) 13 11) 6 12) 12

Part 2 – Using the given information, evaluate the expression.

13) 11 14) 3 15) 0 16) 40 17) 20 18)7

19) 8 20) 4 21) 23 22) 2 23) 3 24) 1

25) 0 26) 6 27) 16 28) 30 29) 15 30)17

31) 5 32) 9 33) 7 34) 4 35) 10 36) 12

37) 8a2−10 b÷ (3 c )+4

2b2÷ (3 a−9 ) when a = −¿3, b = 6, and c = 2

−332

38) [2 y2+8 x2÷ (−10 ) ]÷ 3 z4 x+6 y+8 y+2

when x = 5, y = 7, and z = −¿4−1315

39) (a2+b2) ÷ (5c )10 b−7a−1

when a = −¿8, b = −¿6 and c = 4 −1

Name___________________________________________ Date_________________________ Algebra I – Pd ____ Combining Like Terms 1E

Simplifying and Combining Like Terms Exponent

Coefficient 4x2 Variable (or Base)* Write the coefficients, variables, and exponents of the following:

Like Terms: Terms that have identical variable parts (same variable(s) and same exponent(s)). When simplifying using addition and subtraction, you combine “like terms” by keeping the "like term" and adding or subtracting the numerical coefficients.Examples:

3x + 4x = 7x 13xy – 9xy = 4xy 12x3y2 - 5x3y2 = 7x3y2

Why can’t you simplify? 4x3 + 4y3 11x2 – 7x 6x3y + 5xy3

Simplify the following:1) 7x + 5 – 3x 2) 6w2 + 11w + 8w2 – 15w 3) 6x + 4 + 15 – 7x

4) (12x – 5) – (7x – 11) 5) (2x2 - 3x + 7) – (-3x2 + 4x – 7) 6) 11a2b – 12ab2

WORKING WITH THE DISTRIBUTIVE PROPERTYExample: 3(2x – 5) + 5(3x +6) = Since in the order of operations, multiplication comes before addition and subtraction, we must get rid of the multiplication before you can combine like terms. We do this by using the distributive property:

3(2x – 5) + 5(3x +6) =3(2x) – 3(5) + 5(3x) + 5(6) = 6x - 15 + 15x + 30 =

Now you can combine the like terms: Final answer:

  Coefficients Variables Exponents

8c2     

9x      y8

     12a2b3

     

6x + 15x = 21x 3(2x – 5) + 5(3x + 6) = 21x + 15-15 + 30 = 15

Combining Like Terms Examples:

1) (7 x+8 )+(5 x−10 ) 2) (2 x−5 )+(6+3 x )

3) (9−3 x )−(−6 x+7 ) 4) (7 x+9 )− (8−2 x )

5) (13 u−9)+(8 u+17) 6) (19 a−5 )−(6 a−11 )

7) (7 c2−5 c+10 )−(7 c2−9 c) 8) (16 c2−8+13 c )+ (9−4 c2+7 c )

9) (7 n−13 )−(19 n2−15+12 n ) 10) (22 x2−13 x+7 )+(−9 x2+21x−7 )

11) ( 4 x2−8 x+3 )+(6 x2−4 x+11 ) 12) ( x2−13 x+7 )−(3 x2−4−20 x )

13) (7+x2−4 x )+(10 x2+9 x−5 ) 14) (15+10 x+7 x2)−(−6 x−10 x2+9 )

15) (3 y2−5 y+10 )+( 7 y2−13 y+24 ) 16) (−6 a2+4−9 a )−(5−4 a2+7 a )

17) (3 b4+2b2−8 b+14 )+( 3 b4+16 b−11) 18) (25 z2−9 )−(15 z2+7 z−20 )

19) (6 k3−4 k2+7 k+1 )−(4 k3−3 k2+6k+1 ) 20) (6 x2+13 xy−5 y2 )+(9 xy−2 x2+3 y2 )

21) (5 xy+6 x2 y−4 y2 x )+ (9 x2 y−5 xy+10 x y2 ) 22) (2 x+8 )−(3 x2+5 x−16 )

23) (3 x+7 y−5 )− (2 x2−9x+12 ) 24) (3 y−9x+7 )−(15+8 y−13 x )

25) (15 xy−6 x2 y+9 y2 x )−(9 x2 y+11 xy−4 x y2) 26) (5 z2+10 z )−(−15 z2−18+9 z )

Distributive Property Examples:

1) 4 (7 x−8)+6 (5 x+10) 2) 6(4 x2 – 5 x+2)+3(−8 x2+11 x+4)

3) 5(4 x2 – 8 x+3) –7 (6 x2 – 4 x+11) 4) 4 (6 x3 – 4 x2+1)– 9(4 x3 – 2 x2+1)

5) 10(4 x2+8 x+7) – 8 (5 x2+10 x – 9) 6) 6(4 x2 – 3 x+2)+5(3 x – 6)

7) 9(4 x2 – 7 x+12) –12(3 x2 – 5x – 9) 8) 4 (6 x3 – 4 x2+11) –7(5x2+9)

9) 7(9 x+3 y )+4 (2 x+6) 10) 8(4 x2 – 3 x)+5¿)

11) 6(3x+8)+4(2 x2+9) 12) 5(3+7 y)+6 (8 y – 4 y2)

13) 7(2x+8)– 4 (3 x2+5 x – 6) 14) 9(3 xy+7 y – 5)+5(3 y2+6)

15) 5(3 y2+7 y – 10)+6(2 y2 – 8 y+6) 16) 3(7 x+2 y – 8)– 5(9 x+4 y – 11)

17) 3(12 x4 – 16 x3+4 x2 – 8 x+24)– 4 (9 x4 – 12 x3 – 3 x2 – 6 x+18)Combining Like Terms Examples: ANSWERS

1) 12x -2 2) 5x +1 3) 3x + 2 4) 9x + 1

5)21u + 8 6) 13a + 6 7) 4c + 10 8) 12c2 + 20c + 1

9) -19n2 - 5n + 2 10) 13x2 + 8x 11) 10x2 – 12x + 14 12) -2x2 + 7x + 11

13) 11x2 + 5x + 2 14) 17x2 + 16x + 6 15) 10y2 - 18y + 34 16) -2a2 - 16a – 1

17) 6b4 + 2b2 +8b + 3 18) 10z2 – 7z + 11 19) 2k3 – k2 + k 20) 4x2 – 2y2 + 22xy

21) 15x2y + 6xy2 22) -3x2 – 3x + 24 23) -2x2 + 12x + 7y -17 24) 4x – 5y – 8

25) -15x2y + 13xy2 4xy 26) 20z2 + z + 18

Distributive Property Examples: ANSWERS

1) 58 x+28 2) 3 x2+24

3) −22 x2−12x−62 4) −12 x3+2 x2−5

5) 142 6) 24 x2−3 x−18

7) −3 x+216 8) 24 x3−51 x2−19

9) 71 x+21 y+24 10) 32 x2+6 x−35)

11) 8 x2+18x+84 12) −24 y2+77 y+15

13) −12 x2−6 x+80 14) 27 xy+15 y2+63 y−15

15) 27 y2−13 y−14 16) −24 x−14 y+31

17) 24 x2

Name __________________________________________ Date ________________________ Algebra I – Pd ______ Solving Basic Equations 1F

Solving Equations

Golden Rule of Algebra: “Do unto one side of the equal sign as you will do to the other…”

**Whatever you do on one side of the equal sign, you MUST do the same exact thing on the other side. If you multiply by -2 on the left side, you have to multiply by -2 on the other. If you subtract 15 from one side, you must subtract 15 from the other. You can do whatever you want (to get the x by itself) as long as you do it on both sides of the equal sign.

Solving Single Step Equations:

To solve single step equations, you do the opposite of whatever the operation is. The opposite of addition is subtraction and the opposite of multiplication is division.

Solve the following equations for x:1) x + 5 = 12 2) x – 11 = 19 3) 22 – x = 17

4) 5x = -30 5)x

−5 = 3 6)23 x = - 8

7) x + 15 = 28 8) 15 – x = 21 9)x4 = 5

10) 6 + x = 34 11) 9x = 45 12) 7 + x = 19

Solving Multi-Step Equations:

3x – 5 = 22 To get the x by itself, you will need to get rid of the 5 and the 3. +5 +5 Get rid of addition and subtraction first. ***Use the opposite order of PEMDAS*** 3x = 27 Then, we get rid of multiplication and division. 3 3 x = 9

We check the answer by putting it back in the original equation:Check: 3x – 5 = 22 We have that x = 93(9) - 5 = 22 27 - 5 = 22 22 = 22 (It checks!)

Directions: Solve and check the Multi-Step Equations on looseleaf.

1) 9x - 11 = -38 2) 160 = 7x + 6 3) −x5 +3 = 7

4) ¾x - 11 = 16 5) 4x – 7 = -23 6) 26 = 60 – 2x

7) 21 – 4x = 45 8) x7 - 4 = 4 9) ½ x – 5 = 9

10) 2x + 8 = 34 11) 15 = 3x – 9 12) 33 = 3 – 10x

13) 6x + 15 = 51 14) 19 + 8x = 43 15) x3 + 15 = 48

Name __________________________________________ Date ________________________ Algebra I – Pd ______ Solving Basic Equations 1F

Solving Equations

Front ANSWERS:

1) x = 7 2) x = 30 3) x = 5

4) x = -6 5) x = -15 6) x = -12

7) x = 13 8) x = -6 9) x = 20

10) x = 28 11) x = 5 12) x = 12

Back ANSWERS:

1) x = -3 2) x = 22 3) x = -20

4) x = 36 5) x = -4 6) x = 17

7) x = -6 8) x = 56 9) x = 28

10) x = 13 11) x = 8 12) x = -3

13) x = 6 14) x = 3 15) x = 99

Name___________________________________________ Date_________________________ Algebra I – Pd ____ Like Terms & Basic Equations

Directions: Do all problems on looseleaf.

Part 1 – Simplify the following expression. (Remember to show your RAINBOW!!)

1) 3(5x – 3) + 6(2x + 4) 2) 7(2x2 – 6x + 2) + 3(−¿5x2 + 14x – 4)

3) 9(7x2 – 5x + 9) – 7(8x2 – 3x + 12) 4) 6(3x3 – 4x2 + 11x – 5) – 10(−¿2x3 – 6x2 + 6x +7)

5) 4(2x2 + 6x + 5) – 8(x2 + 3x – 5) 6) 7(4x2 – 3x + 2) + 9(3x – 6)

7) 12(3x2 – 6x + 9) – 9(4x2 – 8x – 12) 8) 5(6x3 – 4x2 + 11) – 6(5x2 + 9)

9) 10(3x4 – 5x3 + 7x2 – 10x + 6) – 5(6x4 – 10x3 – 14x2 – 20x + 12)

Part 2 – Solve for x and check your answers.

1) 2x + 9 = 15 2) 7x – 6 = 29

3) 24 – 2x = −¿12 4) x5 −¿6 = −¿ 8

5) 12x + 2 = −¿34 6) 62 – 4x = 70

7) 88 – 11x = 0 8) 15 = 24 + 3x

9) 13.5x + 2 = −¿25 10) 6x + 2 = 30

11) 2.5x – 9 = 18.5 12) 4x – 12 + 2x = 42