Solving Algebraic Equations with Fractions

Math Lecture: Solving Equations Involving Fractions

Summary

The lecture discussed the process of solving algebraic equations that include fractions. The key method taught was eliminating fractions early in the problem-solving process by multiplying both sides of the equation by the common denominator.

Detailed Notes

• Objective: Simplify and solve equations that include fractions.

• Step-by-Step Approach:

  1. Identify Common Denominator:

     • Determine the least common denominator (LCD) for all fractions in the equation.
     • Example denominators given: 10, 5, 2.
     • Common denominator: 10.

  2. Multiply Entire Equation:

     • Multiply every term of the equation by the common denominator to eliminate fractions.
     • Example equation manipulation: Multiply both sides by 10.

  3. Simplify the Equation:

     • Combine like terms if necessary.
     • For the example problem:
       • Left side (before multiplication): (3x/10) + (2x/5)
       • After multiplying by 10: 3x + 2x * 2 = 5x.
       • Right side becomes 25 after multiplication.

  4. Solve for the Variable:

     • Isolate the variable (e.g., x) by performing appropriate arithmetic operations.
     • Example calculation: 5x = 25 → x = 25 / 5 → x = 5.

  5. Check Your Answer:

     • Substitute the found solution back into the original equation to verify correctness.
     • For x = 5, replug into the equation to ensure both sides are equal.

Verifying Solution Example

• Original equation: (3x/10) + (2x/5) = 2.5
• Plug in x = 5: 1.5 + 2 = 3.5
• Check if LHS equals RHS: You should recalculate original equation values as needed.

By following these steps, fractions in equations can be efficiently handled and solved.