If `(2)/(3)j-(1)/(4)k=(5)/(2)`, what is the value of `8j-3k`?

Explanation

To solve the equation \(\frac{2}{3}j - \frac{1}{4}k = \frac{5}{2}\) and find the value of \(8j - 3k\), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can find the least common multiple (LCM) of the denominators. The denominators here are 3 and 4, and their LCM is 12.

Multiply the entire equation by 12:

\[ 12 \left(\frac{2}{3}j - \frac{1}{4}k\right) = 12 \left(\frac{5}{2}\right) \]

### Step 2: Distribute 12
Now distribute 12 to each term:

\[ 12 \cdot \frac{2}{3}j - 12 \cdot \frac{1}{4}k = 12 \cdot \frac{5}{2} \]

Calculating each term:

\[ 4 \cdot 2j - 3 \cdot k = 6 \cdot 5 \]

This simplifies to:

\[ 8j - 3k = 30 \]

### Step 3: Conclusion
Now we have found that:

\[ 8j - 3k = 30 \]

Thus, the value of \(8j - 3k\) is **30**.

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