Questions: 2/(k-1) = 5/(3k-4)

2/(k-1) = 5/(3k-4)
Transcript text: 24. $\frac{2}{k-1}=\frac{5}{3 k-4}$
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Solution

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Solution Steps

Step 1: Cross-Multiply

Starting with the equation

\[ \frac{2}{k-1} = \frac{5}{3k-4} \]

we cross-multiply to eliminate the fractions:

\[ 2(3k - 4) = 5(k - 1) \]

Step 2: Expand and Rearrange

Expanding both sides gives:

\[ 6k - 8 = 5k - 5 \]

Next, we rearrange the equation to isolate \(k\):

\[ 6k - 5k = -5 + 8 \]

This simplifies to:

\[ k = 3 \]

Final Answer

The solution to the equation is

\(\boxed{k = 3}\).

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