Verified Answer :

  • Multiply both sides by \(-1\) to obtain \(\frac{2}{u} = \frac{24}{25}\).
  • Cross-multiply to reach the equation \(50 = 24u\).
  • Divide by 24 to isolate \(u\), giving \(u = \frac{50}{24}\).
  • Simplify the fraction to arrive at the final answer: \(\boxed{\frac{25}{12}}\).

Explanation

  1. Analysis of the Equation

We are given the rational equation:
\[-\frac{2}{u} = -\frac{24}{25}\]
The variable \(u\) is in the denominator, so it must satisfy the condition \(u eq 0\). Our goal is to solve for \(u\).

  1. Simplifying and Isolating \(u\)

First, we can eliminate the negative sign on both sides by multiplying the entire equation by \(-1\):
\[\frac{2}{u} = \frac{24}{25}\]
To isolate \(u\), we can cross-multiply, which means multiplying the numerator of one side by the denominator of the other side and setting them equal:
\[2 \times 25 = 24 \times u\]
\[50 = 24u\]

  1. Final Calculation and Simplification

Now, divide both sides by 24 to solve for \(u\):
\[u = \frac{50}{24}\]
Finally, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[u = \frac{50 \div 2}{24 \div 2} = \frac{25}{12}\]
Thus, the value of \(u\) is \(\frac{25}{12}\).

Examples

Imagine you are scaling a recipe where the ratio of ingredients is fixed. If the ratio of sugar to flour is represented by \(\frac{2}{u} = \frac{24}{25}\), you can use this algebraic method to determine the exact amount of sugar needed for a given amount of flour. Solving equations like these ensures that proportions are maintained accurately in real-world applications such as cooking, construction, or financial planning.

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