Recording-2025-01-09T18:21:24.373Z

Understanding One-Variable Equations

• One-variable equations can solve various real-world problems by isolating the variable.

• The goal is to manipulate the equation using properties that maintain equality to find the value of the variable.

Problem Example: Temperature Conversion

• Aidan's travel context: Wanting to convert 77 degrees Fahrenheit (F) to Celsius (C).

• Formula Used:

  • F = (9/5)C + 32

    • Where F = degrees in Fahrenheit, C = degrees in Celsius

Steps to Solve the Equation

Step 1: Substitute Known Values

• Substitute 77 for F in the equation to set up our equation:

  • 77 = (9/5)C + 32

Step 2: Isolate the Variable Term

• Use inverse operations to isolate the variable term (9/5)C.

• Operation: Subtract 32 from both sides of the equation:

  • 77 - 32 = (9/5)C

  • 45 = (9/5)C

Step 3: Form a Coefficient of 1

• To get C by itself, multiply both sides of the equation by the reciprocal of (9/5), which is (5/9):

  • 45 * (5/9) = C

  • Calculate the left-hand side:

    • 45 * (5/9) = 25

    • Thus, C = 25

Step 4: Check the Solution

• Verify the solution by substituting C back into the original formula:

  • F = (9/5)(25) + 32

  • Calculate:

    • (9/5 * 25) = 45

    • 45 + 32 = 77 (This confirms our solution is correct)

Final Result

• Conclusion: The Celsius equivalent of 77 degrees Fahrenheit is 25 degrees Celsius.