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Equations and Inequalities
Chapter 4 Equations and Inequalities
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Evaluating and Writing Algebraic Expressions
Lesson 4-1 Evaluating and Writing Algebraic Expressions
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Vocabulary Variable – a symbol that represents one or more numbers
Algebraic expression – a mathematical phrase (number sentence) with at least one variable ***You must THINK your way through this!!
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Writing word Phrases Words: $4 per poster times the number of posters
Expression: · p Written Algebraically: 4p Words: six goals fewer than g goals Expression: Written Algebraically:
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Phrases that mean “ADD”
More than Added to Sum Plus Increased by Others?
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Phrases that mean “Subtract”
Difference of Minus Subtracted from Less than Decreased by Less Others?
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Phrases that mean “Multiply”
Of Groups of Product Times Multiply Twice Others?
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Phrases that mean “Divide”
Quotient Divide Ratio Into Others?
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Write an algebraic expression for the quantity “three more than half a number”.
2. Write an algebraic expression for the quantity “one-fifth of a number reduced by double the same number”.
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3. The number of boxes of cookies sold by Sarah was 43 fewer than the number of boxes of cookies sold by Keiko. The number of boxes of cookies sold by Imelda was 53 more than the number sold by Keiko. Write algebraic expressions for these relations. 4. The first angle of a triangle is 16 degrees less than the second angle. The angle is double the second angle. Write algebraic expressions for these relations.
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5. Kentucky has about half the land area of Minnesota
5. Kentucky has about half the land area of Minnesota. The land area of Maine is approximately two-fifths the land area of Minnesota. Write algebraic expressions for these relations. 6. A census of a middle school found that the number of 7th graders was fifty more than the number of eighth graders. The number of sixth graders was three-fourths the number of eighth graders. Write algebraic expressions for these relations.
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7. In an archery tournament, the number of points awarded for an arrow in the gold circle (bull’s eye) is six less than triple the points awarded for an arrow in the blue ring. Write algebraic expressions for these relations.
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Evaluating Algebraic Expressions
Evaluate for p = 2, n = 3, and s = 5 2p + 7 p + (n · s) 2(2) + 7 Substitute (plug it in) 2 + (3)(5) Solve using PEMDAS 17 11
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Assignment Textbook p. 171 # 12-24/e, 25-30 all, 32-36/e, 40-44
Lesson for Tuesday and Wednesday 1/4 & 1/5
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Using Number Sense to Solve Equations
Lesson 4-2 Using Number Sense to Solve Equations
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Vocabulary Equation – a number sentence with an equal sign
Solution of an equation – the value for a variable that makes the equation true Remember – equal means the same on both sides; balanced
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Solve using Substitution
n – 27 = 38; 11, 51, or 65
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Solve using Mental Math
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Assignment P. 176 # 10-22/e, 23-25, 33, 38-42 {p. 176 # 10, 14, 18, 22, 23, 25, 33, 38, 39, 40, 41, 42} Work for Thursday 1/6 (still due on Friday)
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Solving Equations by Adding or Subtracting
Lesson 4-3 Solving Equations by Adding or Subtracting
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Vocabulary Inverse operations – operations that undo each other to get the variable alone
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Key Concept Addition Property of Equality
If you add the same value to each side of an equation, the two sides remain equal: 20/2=10 so 20/2 + 3 = Subtraction Property of Equality If you subtract the same value to each side of an equation, the two sides remain equal: 12/2=6 so 12/2 -4 = 6 - 4
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Examples
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Assignment Lesson 4-3 P. 183 # 5-29/all, 40-44/all
{p. 183 # 6-28/e, 40-44/all} Tuesday (Due Friday, No time to make up, it’s on this six week’s grade)
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Solving Equations by Multiplying or Dividing
Lesson 4-4 Solving Equations by Multiplying or Dividing
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Key Concept Since multiplication and division are inverse operations, multiplication undoes division and division undoes multiplication. Example: (4 ∙ 9) ÷ 4 = 9 3/5 ∙ 5 = 3
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Examples
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Assignment Lesson 4-4 P. 189 # 9-36/all, 53-57/all
{p. 189 # 10-36/e, 53-57/all} Wednesday
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Exploring Two-Step Problems
Lesson 4-5 Exploring Two-Step Problems
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Vocabulary A(n) _____________ is a mathematical phrase (number sentence) with at least one variable. Algebraic Expression
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Examples Define a variable and write an algebraic expression for the phrase “$10 plus $5 times the number of roses ordered” Define the variable: Let ___= unknown (# roses ordered) Write an algebraic expression:
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Examples Define a variable and write an algebraic expression for “a man is two years younger than three times his son’s age” Define the variable: Let ___= unknown ( ) Write an algebraic expression:
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Assignment Lesson 4-5 P. 197 # 8-12/all, 14-26/e, 27-28, 38-40/all, 43-48/all {p. 197 # 8, 10, 12, 14, 18, 22, 26, 27, 38, 40, 43-48} Tuesday
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Solving Two-Step Problems
Lesson 4-6 Solving Two-Step Problems
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Examples
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Assignment Lesson 4-6 P. 203 # 6-34/e, 43-48
Wednesday
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Graphing Inequalities
Lesson 4-7 Graphing Inequalities
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Examples
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Assignment Lesson 4-7 P. 207 # 8-28/e, 37-41
Thursday (Due Friday )
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Solving Inequalities with Addition and Subtraction
Lesson 4-8 Solving Inequalities with Addition and Subtraction
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Examples
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Assignment Lesson 4-8 P. 212 # 8-32/e, 40-46
Monday (Due Friday )
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Solving Inequalities by Multiplying and Dividing
Lesson 4-9 Solving Inequalities by Multiplying and Dividing
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Examples
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Assignment Lesson 4-8 TEST WEDNESDAY 2-2-11 P. 217 # 6-38/e, 50-53
Monday (Due Wednesday ) TEST WEDNESDAY
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