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Name:__________________________________ Algebra Solving Equations Unit Plan Vocabulary Equation Example Variables Example Inverse Operations Example Solution Example Contradiction Example Identity Example No Solution Example All Real Numbers Example Objective(OLD A.4A, A.1C, A.7B) (4) Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to: (A) find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations; (1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (C) describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations; (7) Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (B) investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities NEW TEKS (2015/2016) PROCESS STANDARDS: A.1A,D,G A.5 Linear functions, equations, and inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions. The student is expected to: (A) solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides ESSENTIAL QUESTION What is the difference between solving and simplifying? PRE-ASSESSMENT Pre-requisite skills: Multiplying by a fraction 1. ½ (4x-6) 2. ¾ (12x+8) Knowledge of Inverse Operations 3. Inverse of addition? ______________ 4. Inverse of Multiplication? ___________ 5. Inverse of Subtraction?_____________ 6. Inverse of Division?_______________ Use order of operations to balance equations 7. 4(x+4)-2= - 1 8. -3(x+3)-8= 5 Knowledge of the difference of an expression and an equation 9. Give an example of an expression:_______________ 10. Give an example of an equation:_________________ SCORE:_______/10 Test 2 Review: Solving 1, 2 & Multi-Step Equations Vocabulary: Define the following words. One Step Equations Video 1. Expression_________________________________________________________ ___________ 2. Equation _______________________________________________________________________ 3. Solution of an Equation ___________________________________________________________ 4. All Real Numbers_________________________________________________________________ 5. No Solution_____________________________________________________________________ SOLVE. Show all work. Circle or box in your answer. 6. 2 x - 9 = - 7 5 9. y 5 3 8 7. 87 – 3x = –13x 8. 4h + 9 = 14 10. 1.2h + 6 = 9.6 11. 4(b – 7) = 4b + 5 12. –6(x – 8) = 78 13. 10x + 4 = 2(5x+2) 14. 3x–5 = 2x–9 15. -6x – 7 = -2(3x + 5) 16. 8x – (6x – 2) = - 2 17. -4(2x-3) = -6x +12 -2x Word Problems 18. Which of the equations below represents the next step of the solution process? Original: 3(5x + 2) + 4 = -35 A. 15x + 2 + 1 = -35 B. 15x + 6 + 12 = -35 C. 15x + 6 + 4 = -35 D. 3( 5x + 6) = -35 19. The sum of eight and twice a number is fourteen. Equation: __________________ Solution: __________________ 20. A photographer charges $50 for a sitting and a basic package of photos. Additional 5 × 7 pictures cost $8 each. How many extra 5 × 7 pictures can you purchase if you spend a total of $96? Equation: __________________ Solution: __________________ 21. Luis deposited $500 into his bank account. He now has $4732. Write and solve an equation to find how much was in his account before the deposit. Equation: __________________ Solution: __________________ 22. Michael bought a beautiful bouquet of flowers for $62.75 (not including tax). If he bought them while there was a 30% off special, what was the original price of the flowers? Equation: __________________ Solution: __________________ 23. The total cost of a DVD was $16.21. If the rate of sales tax was 8.125%, what was the original price of the DVD? Equation: __________________ Solution: __________________ 24. Sara found a great deal on Jolly World tickets where if she purchases a ticket the regular cost of $64, each additional ticket purchased will only cost $48. If the total charge came to $256, how many tickets did she buy? Equation: __________________ Solution: __________________ 25. The width of a rectangle is 9 cm less than twice the length. The perimeter is 72 cm. What is the length and width of the rectangle? Equation: __________________ Solution: __________________ 26. The length of a rectangle is 5 times the width. The perimeter is 84 feet. What is the length and width of the rectangle? Equation: __________________ Solution: __________________ 27. Find the perimeter: this figure? 28. If the value of x is 3 cm, what is the perimeter of x3 + 4y x+ 2 6x3 - y 3x - 2 28. 29. Find the perimeter of the equilateral triangle: 30. If the perimeter is 60 cm, what is the value of x? x+ 2 3x - 2 4w+2 Additional Videos Variables on Both sides Video