Unit 1 Writing and Evaluating Algebraic Expressions
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1 CC Math 1A Name Unit 1 Writing and Evaluating Algebraic Expressions Day Date Lesson Assignment Mon 8/25 Lesson 1 Writing and Evaluating Algebraic Expressions Tues 8/26 Lesson 2 Combining Like Terms & Distributive Property Wed 8/27 Lesson 3 Solving One & Two Step Equations Thurs 8/28 Lesson 4 Solving Multi-Step Equations Fri 8/29 Multi-Step Equations Practice Tues 9/2 Lesson 5 Proportions & Literal Equations Wed 9/3 Lesson 6 Equation Word Problems Thurs 9/4 Equation Word Problems Practice Fri 9/5 Unit 1 Quiz 1 Mon 9/8 Lesson 7 Solving Inequalities Tues 9/9 Solving Inequalities Practice Wed 9/10 Review for Test Thurs 9/11 Test Unit 1 Homework Grade:
2 Common Core Math 1A Unit 1 One-Variable Equations and Inequalities Unit 1 Lesson 1: Writing and Evaluating Algebraic Expressions Name Date:
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16 Common Core Math 1A Unit 1 One-Variable Equations and Inequalities Unit 1 Lesson 3: Solving One and Two Step Equations Name Date: One Step Equations Algebraic Equation: A mathematical sentence that can include numbers, variables, or operation symbols and must have an equal sign. Solution: Any value or values that make an equation true Equivalent Equations: Equations that have the same solution(s). Inverse Operations: Operations that undo one another. Ex: multiplication is the inverse of division, subtraction is the inverse of addition, square rooting is the inverse of squaring, etc. Addition Property of Equality: For any numbers a, b, and c, if a = b, then a + c = b + c. You can add the same thing to both sides of an equation and it will not change the equations. You must keep the scales in balance 3 = = x = 3 + x Subtraction Property of Equality: For any numbers a, b, and c, if a = b, then a c = b c. You can subtract the same thing from both sides on an equation and it will not change the equation. You must keep the scales in balance. 3 = = x = 3 x Multiplication Property of Equality: For any numbers a, b, and c, if a = b, then ac = bc. You can multiply both sides on an equation by the same thing and it will not change the equation. You must keep the scales in balance. 3 = 3 3 * 2 = 3 * 2 3 * x = 3x Division Property of Equality: For any numbers a, b, and c, with c 0, if a = b, then You can divide both sides on an equation by the same thing and it will not change the equation. You must keep the scales in balance. 3 = 3 3/2 = 3/2 3/x = 3/x (x cannot be 0) a c b c.
17 Examples Solve the following Equations m x + 5 = -12 5b = = x u ( 8) = v = 27-13k = y 1 4 p y = 7 x 12 a Two-Step Equations Goal: All variables to one side, and constants to the other. Then multiply or divide. Solve each equation. Check your answer. x y + 1 = -3 x d a 7 2 5k + 16 = 51
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19 Two Step Equations Name Date Prd. In the first column, there are problems worked incorrectly. Use the second column to explain what mistake was made then use the third column to work the problem correctly. Problem Explain Mistake Work Correctly 5x + 18 = -38 5x = -20 x = -4-2x + 8 = -18 2x = x = 26 x = 13 9x 2x = 77 11x = 77 x = 7 -x + 10 = 15 x = 5
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55 Real World Problems 1. Enrique s company pays Sally to advertise on Sally s Website. Sally s website earns $15 per month plus $.05 every time a visitor clicks on the advertisement. What is the least number of clicks per month that Sally needs in order to earn $50 in a month or more? 2. Rosa s cell phone plan costs her $50 a month plus.25$ for each minute she goes beyond her free minutes. How many minutes can she go beyond her free minutes and still pay less than a total of $70? 3. Tara is delivering bags of mulch. Each bag weighs 48 pounds, and the push cart weighs 65 pounds. If her flat-bed truck is capable of hauling 2000 pounds, how many bags of mulch can Tara safely take on each trip? 4. Keith has $500 in savings account at the beginning of the summer. He wants to have at least $200 in the account by the end of the summer. He withdraws $25 each week for food, clothes, and movie tickets. How many weeks can Keith withdraw money from his account.
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