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Mastering Two-Step Equations: A Comprehensive Guide to Solving

This guide delves into the fundamentals of solving two-step equations using inverse operations. Learn how to isolate variables through examples and practical applications, such as calculating costs. Understand the properties of equality and how they apply in problem-solving. Explore step-by-step examples where you will reverse operations to find solutions. With clear definitions, practice problems, and real-world scenarios like budgeting for roses, this guide makes mastering two-step equations both approachable and engaging.

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Mastering Two-Step Equations: A Comprehensive Guide to Solving

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  1. 2.5 Solving Two-Step Equations I can solve two-step equations by using inverse operations.

  2. Requires 2 steps to solve. • Involves 2 operations • Uses properties of equality and inverse operations to solve. • Isolate the variable. • Ex: What is a two-step equation?

  3. Suppose you are ordering roses. Roses cost $5 each and shipping costs $10. Your cost depends on how many roses you buy. • Define your variables • Let r be the number of roses • Shipping is only paid once • 10 + 5r • How many roses did you buy if you spend $70? • 10 + 5r = 70 Writing a two-step equation

  4. Identify operations • Use inverse operations to “undo” them • Undo operations in reverse order • Ex: 2x+3 = 15 • Multiplication and addition • Undo • Subtract 3: 2x = 12 • Divide by 2: x = 6 • Solution: x = 6 How to Solve

  5. Operations • Subtraction and division • Undo • Multiply by 3: x – 7 = -36 • Add 7: -29 • Solution: x = -29 Solving with 2 Terms in the Numerator

  6. -t + 8 = 3 • t = 5 • a = 12 • x = 26 Practice

  7. An advertisement for community service opportunities uses half a sheet of paper per ad and 5 sheets for a title banner. If you have 18 sheets, how many ads can be made? • What do we know? • What are we looking for? • Write an equation. • Solve. • a = 26 Using an Equation as a Model

  8. ODDS ONLY • P.83 #5-37 Assignment

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