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Understanding and Solving Subtraction Equations: A Comprehensive Guide

This guide focuses on solving subtraction equations through various examples and instructional techniques. It covers the process of identifying the variable involved, applying inverse operations to isolate the variable, and utilizing properties of addition to find solutions. Specifically, it includes practical examples such as calculating record high and low temperatures and solving real-world problems involving age differences. Engage with thorough explanations and step-by-step solutions to enhance your understanding of subtraction in algebra.

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Understanding and Solving Subtraction Equations: A Comprehensive Guide

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  1. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 3-3c Objective Solve subtraction equations

  4. Example 3-3c Vocabulary None

  5. Lesson 3 Contents Example 1Solve an Equation by Adding Example 2Solve a Subtraction Equation Example 3Use an Equation to Solve a Problem

  6. Example 3-1a Write the equation. Ask “what is being done to the variable?” The variable is being subtracted by 5 x – 5 + 5 = 10 + 5 Do the inverse on each side to “undo” the subtraction Bring down x - 5 Add 5 Bring down = 10 Add 5 1/3

  7. Example 3-1a Bring down x Combine “like” terms Bring down = Combine “like” terms x – 5 + 5 = 10 + 5 Use the Identity Property of Addition to add x + 0 x + 0 = 15 Answer: x = 15 1/3

  8. Example 3-1c Answer: w = 12 1/3

  9. Example 3-2a Write the equation. Ask “what is being done to the variable?” The variable is being subtracted by 5 = -1 + 5 x – 5 + 5 Do the inverse on each side to “undo” the subtraction Bring down x - 5 Add 5 Bring down = -1 Add 5 2/3

  10. Example 3-2a Bring down x Combine “like” terms Bring down = Combine “like” terms = -1 + 5 x – 5 + 5 Use the Identity Property of Addition to add x + 0 x 4 + 0 = Answer: x = 4 2/3

  11. Example 3-2b Answer: d = 3 2/3

  12. Example 3-3a The difference between the record high and the record low temperatures in Oregon is 173F. The record low temperature is –54F. What is the record high temperature in degrees Fahrenheit? Determine process to use Difference = high - low = x 173 The word “difference” tells us we need to subtract Replace “difference” with 173 Bring down = Replace “high” with variable 3/3

  13. Example 3-3a The difference between the record high and the record low temperatures in Oregon is 173F. The record low temperature is –54F. What is the record high temperature in degrees Fahrenheit? Difference = high - low Bring down - = x - (- 54) Replace “low” with -54 173 Remember: With 2 negative signs, put them together to make addition 173 = x + 54 3/3

  14. Example 3-3a Ask “what is being done to the variable?” Difference = high - low The variable is being added by 54 173 = x - (- 54) 173 = x + 54 Do the inverse on each side to “undo” the addition 173 - 54 - 54 = x + 54 Bring down 173 Subtract 54 Bring down = x + 54 Subtract 54 3/3

  15. Example 3-3a Combine “like” terms Difference = high - low Bring down = x 173 = x - (- 54) Combine “like” terms 173 = x + 54 Use the Identity Property of Addition to add x + 0 173 - 54 - 54 = x + 54 Add dimensional analysis 119 = x + 0 What is the record high temperature in degrees Fahrenheit? Answer: 119 = x 0 F 3/3

  16. Example 3-3c * The difference between the age of Julie’s mother and Julie’s age is 27 years. Julie’s age is 6. What is the age of Julie’s mother? Answer: x = 33 years NOTE: Could also be 33 years = x 3/3

  17. End of Lesson 3 Assignment

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