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(a+b/c)(d)=f Solve For A

2 min read Jun 16, 2024
(a+b/c)(d)=f Solve For A

Solving for 'a' in the Equation (a + b/c)(d) = f

This article will guide you through the steps to solve for 'a' in the equation (a + b/c)(d) = f.

Understanding the Equation

The equation represents a scenario where you are multiplying a sum of two terms by a constant 'd', and the result is equal to 'f'. Our goal is to isolate 'a' on one side of the equation.

Step-by-Step Solution

  1. Distribute: Start by distributing the 'd' across the terms inside the parentheses:

    ad + (b/c)d = f

  2. Simplify: Combine the terms with 'd':

    ad + bd/c = f

  3. Isolate 'ad': Subtract 'bd/c' from both sides of the equation:

    ad = f - bd/c

  4. Solve for 'a': Finally, divide both sides of the equation by 'd' to isolate 'a':

    a = (f - bd/c) / d

Simplifying the Solution

You can further simplify the solution by finding a common denominator for the terms in the numerator:

a = (cf - bd) / cd

Final Result

The solution for 'a' in the equation (a + b/c)(d) = f is:

a = (cf - bd) / cd

Key Points to Remember

  • This solution assumes that 'c' and 'd' are non-zero values. If either 'c' or 'd' is zero, the equation becomes undefined.
  • You can apply this method to solve for any variable in similar equations. Just remember to isolate the variable you want to solve for by using algebraic operations.

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