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(4)/(9)(16 X-1)-(4x-(1+x)/(9))=(1)/(9)x(16)/(9)

3 min read Jun 16, 2024
(4)/(9)(16 X-1)-(4x-(1+x)/(9))=(1)/(9)x(16)/(9)

Solving the Equation: (4/9)(16x - 1) - (4x - (1 + x)/9) = (1/9)x(16/9)

This equation might look intimidating at first, but with a few steps, we can simplify it and find the solution for 'x'. Let's break down the process:

1. Simplifying the Equation

  • Distribute: Start by distributing the constants outside the parentheses:

    (64/9)x - (4/9) - 4x + (1 + x)/9 = (16/81)x

  • Combine like terms: Combine the 'x' terms and the constant terms:

    (64/9)x - 4x + (1 + x)/9 - (4/9) = (16/81)x

    (28/9)x + (1 + x)/9 - (4/9) = (16/81)x

  • Simplify the fraction: Combine the fractions with the same denominator:

    (28/9)x + (1 + x - 4)/9 = (16/81)x

    (28/9)x + (x - 3)/9 = (16/81)x

2. Isolating 'x'

  • Move 'x' terms to one side: Subtract (16/81)x from both sides:

    (28/9)x - (16/81)x + (x - 3)/9 = 0

  • Find a common denominator: To combine the 'x' terms, find a common denominator for the fractions:

    (224/81)x - (16/81)x + (x - 3)/9 = 0

    (208/81)x + (x - 3)/9 = 0

  • Combine 'x' terms:

    (208/81)x + (9/81)x - (3/9) = 0

    (217/81)x - (1/3) = 0

  • Isolate 'x': Add (1/3) to both sides:

    (217/81)x = (1/3)

  • Solve for 'x': Multiply both sides by (81/217):

    x = (1/3) * (81/217)

    x = 27/217

Conclusion

The solution to the equation (4/9)(16x - 1) - (4x - (1 + x)/9) = (1/9)x(16/9) is x = 27/217. By systematically simplifying the equation and isolating 'x', we were able to find the solution.

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