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Chapter 1 Review College Algebra

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Remember the phrase “Please Excuse My Dear Aunt Sally” or PEMDAS. ORDER OF OPERATIONS 1. Parentheses - ( ) or [ ] 2. Exponents or Powers 3. Multiply and Divide (from left to right) 4. Add and Subtract (from left to right)

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Evaluate 7 + 4 3. Is your answer 33 or 19? You can get 2 different answers depending on which operation you did first. We want everyone to get the same answer so we must follow the order of operations.

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Once again, evaluate 7 + 4 3 and use the order of operations. = 7 + 12(Multiply.) = 19 (Add.)

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Example #1 14 ÷ 7 2 - 3 = 2 2 - 3 (Divide l/r.) = 4 - 3 (Multiply.) = 1(Subtract.)

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Example #2 3(3 + 7) 2 ÷ 5 = 3(10) 2 ÷ 5(parentheses) = 3(100) ÷ 5(exponents) = 300 ÷ 5(multiplication) = 60(division)

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Example #3 20 - 3 6 + 10 2 + (6 + 1) 4 = 20 - 3 6 + 10 2 + (7) 4(parentheses) = 20 - 3 6 + 100 + (7) 4(exponents) = 20 - 18 + 100 + (7) 4 (Multiply l/r.) = 20 - 18 + 100 + 28 (Multiply l/r.) = 2 + 100 + 28 (Subtract l/r.) = 102 + 28 (Add l/r.) = 130(Add.)

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Which of the following represents 11 2 + 18 - 3 3 · 5 in simplified form? 1. -3,236 2. 4 3. 107 4. 16,996 Answer Now

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Simplify 16 - 2(10 - 3) Answer Now 1. 2 2. -7 3. 12 4. 98

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Simplify 24 – 6 · 4 ÷ 2 Answer Now 1. 72 2. 36 3. 12 4. 0

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1.substitute the given numbers for each variable. 2.use order of operations to solve. Evaluating a Variable Expression To evaluate a variable expression:

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Example # 4 n + (13 - n) 5 for n = 8 = 8 + (13 - 8) 5 (Substitute.) = 8 + 5 5 (parentheses) = 8 + 1 (Divide l/r.) = 9 (Add l/r.)

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Example # 5 8y - 3x 2 + 2n for x = 5, y = 2, n =3 = 8 2 - 3 5 2 + 2 3 (Substitute.) = 8 2 - 3 25 + 2 3 (exponents) = 16 - 3 25 + 2 3 (Multiply l/r.) = 16 - 75 + 2 3 (Multiply l/r.) = 16 - 75 + 6 (Multiply l/r.) = -59 + 6 (Subtract l/r.) = -53 (Add l/r.)

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What is the value of -10 – 4x if x = -13? Answer Now 1. -62 2. -42 3. 42 4. 52

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What is the value of 5k 3 if k = -4? Answer Now 1. -8000 2. -320 3. -60 4. 320

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What is the value of if n = -8, m = 4, and t = 2 ? Answer Now 1. 10 2. -10 3. -6 4. 6

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An expression is NOT an equation because it DOES NOT have an equal sign. There are 2 types of expressions. 5 + 84 Numerical 3x 3x + 10 Algebraic Notice there are no equal signs in these expressions so they are not equations !

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A numerical expression contains only numbers and symbols and NO LETTERS. 5 times 3 plus 8 (53) + 8

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An algebraic expression contains only numbers, symbols, and variables. It is sometimes referred to as a variable expression. The product of 3 and x 3x The sum of m and 8 m + 8 The difference of r and 2 r - 2

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What is a variable? A variable represents an unknown value. 1) 4 + x 2) 10 – ? 3) 5y 4) 20 A variable can be any letter of the alphabet since it represents an unknown.

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Word Phrases for multiplication are: The product of 5 and a number c Seven times a number t 6 multiplied by a number d 5 c or 5c 7 t or 7t 6 d or 6d

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The Placement rule for multiplication is: The product of 5 and a number c Seven times a number t 6 multiplied by a number d 5 c or 5c 7 t or 7t 6 d or 6d Always write the variable AFTER the number.

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Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. m = 2 6 + m ? 6 + 2 8

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Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. r = 3 7 + r ? 7 + 3 10

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Evaluate the variable expression when n = 6. 1)2) Evaluate just means solve by substitution.

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Evaluate the variable expression when n = 6. Evaluate just means solve by substitution. 3) 4)

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Evaluate the algebraic expression when n = 8. 1)2)

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Evaluate the expression if a = 3 and b = 4. 1)2)

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Evaluate the expression if a = 3 and b = 4. 3)4)

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Evaluate the expression if x = 5 and y = 3. 1) 2)

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#2 Show the substitution. Show your work down. Circle your answer. Show your work one step at a time down. No equal signs! Evaluate means solve. Evaluate i f x = 3 and y = 4

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Combining Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms. Like terms include letters that are the same and numbers.

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Let ’ s try one… Step One: Write the expression. 4x + 5x -2 - 2x + 7 Collect all the terms together which are alike. Remember that each term comes with an operation (+,- ) which goes before it. 4x, 5x, and -2x -2 and 7 Simplify the variable terms. 4x+5x-2x = 9x-2x = 7x Simplify the constant (number) terms. -2+7 = 5 You have a simplified expression by writing all of the results from simplifying. 7x + 5

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Another example… 10x – 4y + 3x 2 + 2x – 2y 3x 2 10x, 2x -4y – 2y 3x 2 + 12x – 6y Remember you cannot combine terms with the same variable but different exponents.

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Now you try… Simplify the following: 5x + 3y - 6x + 4y + 3z 3b - 3a - 5c + 4b 4ab – 2a 2 b + 5 – ab + ab 2 + 2a 2 b + 4 5xy – 2yx + 7y + 3x – 4xy + 2x A A A A

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You Try #1 Simplify the following: 1. 5x + 3y - 6x + 4y + 3z 5x, -6x 3y, 4y 3z -x + 7y + 3z

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You Try #2 Simplify the following: 2. 3b - 3a - 5c + 4b 3b, 4b -3a -5c -3a + 7b – 5c

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You Try #3 Simplify the following: 3. 4ab – 2a 2 b + 5 – ab + ab 2 + 2a 2 b + 4 4ab, -ab -2a 2 b, 2a 2 b 5, 4 ab 2 3ab + ab 2 + 9

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You Try #4 Simplify the following: 4. 5xy – 2yx + 7y + 3x – 4xy + 2x 5xy, -2yx, -4xy 7y 3x, 2x -xy + 7y + 5x

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by Mr. Fitzgerald

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Five Properties 1.Distributive 2.Commutative 1.“order doesn’t matter” 3.Associative 1.“grouping doesn’t matter” 4.Identity properties of one and zero 5.Inverse “opposite”

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(2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition 1.

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3 + 7 = 7 + 3 Commutative Property of Addition 2.

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8 + 0 = 8 Identity Property of Addition 3.

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6 4 = 4 6 Commutative Property of Multiplication 5.

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17 + (-17) = 0 Inverse Property of Addition 6.

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2(5) = 5(2) Commutative Property of Multiplication 7.

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3(2 + 5) = 32 + 35 Distributive Property 9.

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6(78) = (67)8 Associative Property of Multiplication 10.

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5 1 = 5 Identity Property of Multiplication 11.

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(6 – 3)4 = 64 – 34 Distributive Property 13.

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1(-9) = -9 Identity Property of Multiplication 14.

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3 + (-3) = 0 Inverse Property of Addition 15.

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1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of Addition 16.

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-3(6) = 6(-3) Commutative Property of Multiplication 17.

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-8 + 0 = -8 Identity Property of Addition 18.

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37 – 34 = 3(7 – 4) Distributive Property 19.

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6 + [(3 + (-2)] = (6 + 3) + (- 2) Associative Property of Addition 20.

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7 + (-5) = -5 + 7 Commutative Property of Addition 21.

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(5 + 4)9 = 45 + 36 Distributive Property 22.

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-3(5 4) = (-3 5)4 Associative Property of Multiplication 23.

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-8(4) = 4(-8) Commutative Property of Multiplication 24.

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5 1 / 7 + 0 = 5 1 / 7 Identity Property of Addition 25.

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3 / 4 – 6 / 7 = – 6 / 7 + 3 / 4 Commutative Property of Addition 26.

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1 2 / 5 1 = 1 2 / 5 Identity Property of Multiplication 27.

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-8 2 / 5 + 0 = -8 2 / 5 Identity Property of Addition 29.

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[(- 2 / 3 )(5)]9 = - 2 / 3 [(5)(9)] Associative Property of Multiplication 30.

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6(3 – 2n) = 18 – 12n Distributive Property 31.

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2x + 3 = 3 + 2x Commutative Property of Addition 32.

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ab = ba Commutative Property of Multiplication 33.

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a + 0 = a Identity Property of Addition 34.

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a(bc) = (ab)c Associative Property of Multiplication 35.

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a1 = a Identity Property of Multiplication 36.

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a +b = b + a Commutative Property of Addition 37.

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a(b + c) = ab + ac Distributive Property 38.

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a + (b + c) = (a +b) + c Associative Property of Addition 39.

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a + (-a) = 0 Inverse Property of Addition 40.

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