Math Antics Lecture: Solving Algebraic Equations with Multiplication and Division

Key Concepts

• Inverse Operations: Just as addition and subtraction are inverse operations, multiplication and division are inverse operations which can undo each other.
• Rearranging Equations: The goal is to isolate the unknown variable on one side of the equation. To do this, perform the inverse operation on both sides of the equation to keep it balanced.

Solving Equations with Multiplication

• If an unknown variable is being multiplied by a number, divide both sides by that number to isolate the variable.

Example

• Equation: 3x = 15

  • Step 1: Divide both sides by 3.
    • Left side: 3x ÷ 3 = x
    • Right side: 15 ÷ 3 = 5
  • Solution: x = 5

• Equation: 12x = 96

  • Step 1: Divide both sides by 12.
    • Left side: 12x ÷ 12 = x
    • Right side: 96 ÷ 12 = 8
  • Solution: x = 8

Solving Equations with Division

• If an unknown variable is being divided by a number, multiply both sides by that number to isolate the variable.

Example

• Equation: x ÷ 2 = 3

  • Re-written: \frac{x}{2} = 3
  • Step 1: Multiply both sides by 2.
    • Left side: \frac{x}{2} * 2 = x
    • Right side: 3 * 2 = 6
  • Solution: x = 6

• Equation: x ÷ 10 = 15

  • Re-written: \frac{x}{10} = 15
  • Step 1: Multiply both sides by 10.
    • Left side: \frac{x}{10} * 10 = x
    • Right side: 15 * 10 = 150
  • Solution: x = 150

Tricky Division - Unknown in Denominator

• If the unknown is in the denominator, the procedure changes as division does not have the commutative property.

Example

• Equation: 4 ÷ x = 2 or \frac{4}{x} = 2
  • Step 1: Multiply both sides by x.
    • Left side: 4 = 2x
  • Step 2: Divide both sides by 2 to solve for x.
    • Left side: 4 ÷ 2 = 2
    • Right side: 2x ÷ 2 = x
  • Solution: x = 2

Conclusion

• Practice is crucial for mastering solving one-step algebraic equations.
• Re-watch the videos if necessary to grasp the concepts thoroughly.

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