Lecture Notes: Addition Property of Equality

Introduction

• Topic: Addition property of equality in solving one-step equations.
• Key Concept: What you do on one side of the equation must be done on the other side to maintain the integrity of the equal sign.

Example Problems

Problem 1

• Equation: Solve for m when m - 5 = 9.
• Steps:
  1. Identify the variable (in this case, m) and the number attached to it (-5).
  2. Recognize that the inverse of -5 is +5.
  3. Add 5 to both sides to maintain equality:
     • Left side: m - 5 + 5 = 0 (since -5 and +5 cancel each other out)
     • Right side: 9 + 5 = 14
  4. Simplified equation: m = 14
• Verification: Substitute m = 14 back into the original equation to ensure both sides equal 9.

Problem 2

• Equation: Solve for b in 12 + b = 29.
• Steps:
  1. Identify b with the attached number -12 (opposite side scenario).
  2. Inverse of -12 is +12.
  3. Add 12 to both sides:
     • Left side: -12 + 12 = 0
     • Right side: 17 + 12 = 29
  4. Simplified equation: b = 29
• Verification: Substitute b = 29 back into the equation to check if -12 + 29 equals 17.

Key Points

• Inverse Operations: Adding the inverse of a number cancels it out, simplifying the equation.
• Checking Work: Always substitute the solution back into the original equation to verify correctness.
• Consistency: Keep the equal signs aligned and ensure operations are mirrored on both sides.

Conclusion

• Summary: These problems illustrate the one-step process using the addition property of equality.
• Advice: Ensure that each step is performed on both sides of the equation to maintain balance and verify solutions by substituting them back into the original problem.