Math Antics: Solving Simple Algebraic Equations with Addition and Subtraction

Introduction

• Algebra involves equations with variables or unknown values.
• Solving an equation means finding the values of these unknowns.
• Focus of this video:
  • Simple equations involving addition and subtraction.
  • Next video will cover multiplication and division.

Key Strategy for Solving Equations

• Objective: Rearrange the equation so the unknown is isolated on one side of the equal sign.
• Balance Concept:
  • An equation is like a balance scale.
  • Both sides must have equal values to stay balanced.

Maintaining Balance in Equations

• Any change to one side must be mirrored on the other side.
• Operations include addition, subtraction, multiplication, and division.
  • Example: If adding a number to one side, add the same to the other.

Solving Equations with Addition

1. Example: x + 7 = 15

   • Isolate 'x' by subtracting 7 from both sides.
   • Equation becomes x = 8.
   • Verification: Replace 'x' in original equation (8 + 7 = 15).

2. Example: 40 = 25 + x

   • Subtract 25 from both sides to isolate 'x'.
   • Equation becomes x = 15.

Solving Equations with Subtraction

1. Example: x - 5 = 16

   • Add 5 to both sides to isolate 'x'.
   • Equation becomes x = 21.

2. Example: 10 = x - 32

   • Add 32 to both sides to isolate 'x'.
   • Equation becomes x = 42.

Tricky Variation of Subtraction

• Example: 12 - x = 5
  • Challenge: Subtraction is not commutative.
  • Solution: Add 'x' to both sides first (12 = 5 + x).
  • Then subtract 5 from both sides to solve (x = 7).

Conclusion

• Process is consistent for all types of numbers (integers, decimals, fractions).
• Practice is crucial to understanding.
• Supports different symbols for unknowns.

Reminder: Practice solving basic equations to reinforce learning.

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