HG

Recording-2025-01-09T18:26:27.197Z

Understanding Properties of Equality

  • Equal Sign: Does not indicate a direct answer; it shows that the values are the same on both sides.

Solving the Equation: Two Methods

Method 1: Isolating the Variable

  • Step 1: Isolate the variable term:

    • Subtract 32 from both sides.

  • Step 2: Get the coefficient to equal 1:

    • Multiply by the reciprocal on both sides.

    • Result: 25 = c

Method 2: Clearing the Fraction

  • Goal: Get rid of the fraction by multiplying by a factor that will eliminate it.

  • Step 1: Multiply the entire equation by 5:

    • Left side: 5(77) = 385.

    • Right side: Use distributive property: 5(9c + 160) = 9c + 160.

  • Step 2: Isolate the variable term:

    • Subtract 160 from both sides.

  • Step 3: Get the coefficient of the variable term to equal 1:

    • Divide both sides by 9.

    • Result: 25 = c

Conclusion

  • Both methods yield the same result (25 = c), showcasing different approaches to solving equations.

  • Alternative method of multiplying each term by 5/9 could clear the fraction but may introduce additional fractions.